That is, of course, a valid question, and to address it I will first briefly discuss some other religions and and why I would not accept them as true. Then I will give a few reasons why Christianity does the best job of explaining what we see and experience, and why it is the best fit from the standpoint of rationality and morality. Of course this is going to be very cursory because the subject matter is so broad, but I would be happy to discuss it further in the comments.
Deism: Deists believe that an intelligence designed the universe, but they do not believe in a personal God who intervenes in his creation. The supreme being of deism simply created the universe and left it alone.
The chief problem of deism is that it leaves so many unanswered questions, like why a creative intelligence would have no revealed purpose. In spite of the problem of evil, this universe is pretty impressive. Would a supremely high intelligence create and then simply not care? I suppose that's possible, but then he would be nothing like us, his most intelligent creatures (as far as we know), because we have an innate sense that our actions should be purposeful and life should have meaning. And most talented creators put much of themselves into their creations, so we would expect that the intelligence behind this universe would reveal himself in his creation, and particularly in his intelligent creatures.
Primitive polytheistic religions: These are probably the easiest to dismiss because most modern cultures have outgrown them. If a religion is true, even the most highly developed intellect would be stretched in trying to understand it. It has to be "higher" than our ways, but not "different" in that it violates the rules of logic or our sense of morality. Since civilization has outgrown these religions, that indicates that they are manmade.
Judaism: Judging from the comments on Atheist Central and Dwindling in Unbelief, I don't expect that Judaism appeals much to most atheists. They often use the Old Testament as ammunition against Christianity, particularly by claiming that it violates a modern sense of morality.
This is a valid argument, because the Old Testament laws were often strange and problematic, and they seemed based on primitive cultures. I recognize, of course, that this is a potential problem for Christianity as well as for Judaism, so the question is how each religion addresses it.
Jews differ in terms of how literally they interpret the Jewish law, with Orthodox Jews taking it the most literally while Reform Jews consider the Jewish law to merely provide guidelines. But what is the point of the Jewish law if it can be watered down however we want? This is moral relativism, and it also conflicts with the nature of YHWH, who had very strict rules and clearly established his holiness in the Old Testament.
Christianity does not allow for watering down of any of its teachings, but the New Testament instructs us on how to interpret the Old Testament. This is a more rational and systematic approach than simply glossing over difficulties.
Luke 24:27 says, "Then beginning with Moses and with all the prophets, [Jesus] explained to them the things concerning Himself in all the Scriptures." The entire Old Testament is full of symbolism or prophesies of Christ, starting with the very first chapter of Genesis. Colossians 2:16 says that the ceremonial laws of the Old Testament "are a mere shadow of what is to come, but the substance belongs to Christ." Jesus said, "Do not think I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill." So even though none of the Old Testament authors understood it at the time, because it was a hidden mystery (Colossians 1:26), they all wrote of God coming in the flesh, and he was the fulfillment of the Law and the Prophets.
Islam: The Qur'an was dictated by Mohammed, who claimed to have received it as a direct revelation from the angel Gabriel. Mohammed is considered the greatest of a number of prophets, including Moses and Jesus.
There are several ways in which Islam has less of a ring of truth than Christianity. First, it seems unlikely that God would entrust his entire revealed word to one person. The Bible, on the other hand, consists of writings by at least forty authors. (This criticism extends to Mormonism as well, which I will not discuss further.) Second, Mohammed was supposedly the greatest and most virtuous of all the prophets, and close to perfection. Still, he married a nine-year-old girl, which may or may not have been a problem in that culture, but now we know how psychologically damaging that would be to a child.
Compare that to Jesus, who challenged all social convention with a transcendent and timeless morality. In spite of his culture, Jesus treated women with respect (John 4) and children with the love and acceptance they need (Matthew 19:13-15). He had the courage to stand up to hypocritical scribes and Pharisees (Matthew 23). He ate and drank with prostitutes and notorious sinners, but instead of conforming to their behavior he transformed their lives (Matthew 11:19). He was sexually self-controlled without being uptight (Luke 7:37-48). He was, as Mahatma Gandhi said, "a beautiful example of the perfect Man."
Another problem with Islam is that the Qur'an makes specific scientific allegations that are known to be false while also claiming a high level of infallibility. For example, it tells a story of how a Muslim discovered that the sun sets in a pool of murky water. It also says that the earth is held in place by mountains, and that Allah holds up the sky so that it doesn't fall on us. These are explanations, not poetry, and they clearly indicate that the sky is a hard dome and the earth is flat.
Chapter 1 of Genesis, on the other hand, contains semi-poetical language, and the first few chapters of Genesis are full of deep symbolism of free will, sin, Christ and the church, redemption, and eternal life--and much of the same symbolism continues in Revelation. The message is primarily theological, and any cosmological or biological truths would be secondary. Unlike Mohammed, Jesus never teaches anything about science. All his teaching pertains to the kingdom of God. Nothing in the Bible has been falsified by science because the controversial passages are so highly symbolic.
Buddhism and Taoism: These are more philosophies than religions, in the sense that they do not teach anything about God or gods. So if someone suspects that the universe was created, Buddhism and Taoism do not give further information.
Hinduism: Hinduism is amorphous, in that it encompasses polytheism, monotheism, atheism, and pantheism. I think it would appeal more to someone who is looking for self-fulfillment than someone who is searching for objective truth.
Hindus also either believe that the universe is eternal or that there is an endless cycle of universes. The idea that the universe is eternal is inconsistent with modern science, and the notion that any other universe than ours has existed is not supported by evidence.
New Age spirituality: This is a make-it-yourself religion that retains the spiritual mysticism that deism rejects. Again, there is no objective truth to be found in this type of spirituality.
All of these religions are either a) too rigid and therefore dated, or b) too amorphous and therefore whatever we want to make them. Judaism and Islam are too rigid and they can also seem harsh and legalistic. The others are too soft and let us shape our deity into whatever we want him to be. The god of these religions never offends and never makes difficult claims, nor does he seem to care much.
Why is Christianity more consistent with the evidence?
The moral standard: Jesus said, "'You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.' This is the great and foremost commandment. The second is like it, 'You shall love your neighbor as yourself.' On these two commandments depend the whole Law and the Prophets" (Matthew 22:37-40).
So on the one hand, Jesus set a very high moral standard, but on the other hand, it is not rigid or harsh. In other words, we are not to live according to the strict rules of the Old Testament, but by the wisdom that comes from faith in Christ, and that always has as its chief goal the glory of God and the good of others. And the New Testament elaborates on what that means in practical terms. Galatians 5:22 says: "The fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law." These qualities are indisputably good by any standard.
Furthermore, Christian theology also recognizes that we do not naturally have the power to love like this, so we need to be born of the Spirit of God who will do the good work through us. This is the nature of faith. Galatians 5:6 says, "The only thing that counts is faith expressing itself through love." In other words, salvation is by faith, but love is the evidence of faith. If we belong to Christ, we will resemble him, because his Spirit will work in and through us.
The combination of complexity and simplicity: The message of salvation is very simple: We are to come to Christ as broken sinners and he heals us by the power of the Holy Spirit. The more humble and needy we are, the better qualified we are to receive this gift of eternal life. Pride is the only barrier.
However, Christian theology is also extremely complex and nuanced. It never oversimplifies what is not simple, and God is not simple, nor is human nature. The Bible is inherently logical, but the logic is not evident on a superficial level. It contains many subtleties and paradoxes that make more and more sense over time, like an infinitely complex puzzle that we will never solve in this life, but which has a very definite order and logic. It mirrors the natural world in this respect, which would indicate that the Christian God is the creator of the world.
A holy God of love: The God of the Bible is holy and he "dwells in unapproachable light" (1 Timothy 6:16), but he loves us so much that he uses the imagery of marriage to describe the fulfillment of his plan of redemption. This begins with Adam and Eve foreshadowing Christ and the church (Ephesians 5:32), it is further symbolized in the Song of Solomon, and it reaches its fulfillment in Revelation (Revelation 21:9-11).
The idea that a god should be loving comes from Christianity. No other religion talks about a personal God whose nature is love, and certainly not a holy God who is so humble that he assumed the role of a servant and washed his disciples' feet.
Freedom: Muslim extremists have come under fire for threatening violence against anyone who draws Mohammed. In defense of Islam, they prohibit drawing any of their prophets, including Moses and Jesus. However, this kind of legalism is antithetical to Christianity, which calls us to freedom, even with the associated consequences. No other church was rebuked more severely by Paul than the one in Galatia, which had fallen from grace into legalism.
2 Corinthians 3:17 says, "Now the Lord is the Spirit, and where the Spirit of the Lord is, there is liberty." Where Christianity is practiced the way it should be (i.e., where the Holy Spirit is leading) there will be no coercion, manipulation, or brainwashing. Free will is central to our humanity, and in salvation that humanity is perfected, so we become more and more free the more we become like Christ. But freedom in Christianity doesn't mean lawlessness--it means being governed by an internal law that comes from the presence of the Holy Spirit. Galatians 5:13 says: "For you were called to freedom, brethren; only do not turn your freedom into an opportunity for the flesh, but through love serve one another."
This premium on freedom is consistent with what we see, and it indicates that the Christian God is our creator. We have free will and recognize its importance, but it is also the source of much of the evil and suffering in the world.
The problem of evil: After Anthony Flew became a deist, Christianity was the religion he considered most seriously, but he rejected it because of the problem of evil. The problem of evil is the major reason why deists believe in an intelligence that created and left us to fend for ourselves. If he exists, they reason, he couldn't possibly care.
But the God of Christianity does care; the entire Bible is about the problem of evil. In the opening chapters of Genesis we see its cause: free will and sin. In the Gospel accounts we see its cure: the cross. And in Revelation 21:3-4 we see the final outcome: "Behold, the tabernacle of God is among men, and He will dwell among them, and they shall be His people, and God Himself will be among them, and He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away."
Christianity is the only religion that takes the problem of evil so seriously that God himself became one of us and died the most profane death possible so that he could solve it. He satisfied the requirements of the Law on our behalf and paid the penalty for the sins of the world, and in that sacrifice he bridged the gap between a holy God and fallen humanity. This means that we can all receive his Holy Spirit, who will make us like him while preserving our individuality and our freedom.
God has freely chosen to give us abundant life that not even physical death can sever, and some day he will create "new heavens and a new earth in which righteousness dwells" (2 Peter 3:13), where he will fulfill the deepest human longings. Nobody who does any harm can have a place in that new creation (Isaiah 11:9, 65:25), because otherwise the problem of evil would persist. But God has, through the cross, solved the problem forever, and the suffering of this life will become just a faint memory.