Perhaps the most unique characteristic of the Christian God is that He exists. The other ones don't. Of course, that is a matter of profound debate, as we all know.
I would say the chief and most critical differences have to do, ultimately, with the Christian God's character of holiness. You're going to get an argument on this from other people who will say that their gods are holy, too. What is unique about Christianity among all the world religions is its central doctrine of a once-for-all atonement that is offered to people to grant them salvation. Old Testament Judaism had a provision for the atonement of sin, but most religions have no provision for an atonement, basically because they do not consider it to be a prerequisite for redemption.
My question is, Why would a world religion not consider an atonement necessary for redemption unless, in their view, God is less than holy? If God is perfectly just and people are not perfectly just, yet those people are trying to be in a vital relationship with God, you have a basic, overwhelming problem. How would a God who is holy and just accept in his presence unjust creatures? That's what Judaism and Christianity understand as the vital problem. Human beings who are unjust must be justified somehow to enter the presence of a holy God. That's why the whole focus of Judeo-Christianity is at the point of atonement, which brings about reconciliation.
But if you don't believe that God is all that holy, there's no need for any concept of reconciliation. We can live however we want because this kind of god is a cosmic bellhop who will overlook all of our sins and do whatever we want him to do for us. I would say the holiness of God is the vital difference
~ R.C. Sproul, Now - That's a Good Question!
Charles Haddon Spurgeon, a British preacher and evangelist of the 19th century, once said, "Sooner could a fish live in a tree, than a sinner in the presence of a holy God." Most world religions propose a standard of living - a code of conduct if you will - whereby one can be acceptable to their god.
But your Christian Bible says, "All have sinned, and come short of the glory of God." (Romans 3:23) And Jesus Himself said, "I am the way, the truth, and the life: no man cometh unto the Father, but by me." (John 14:6).
So ... the difference? Jesus said that we cannot make ourselves acceptable to God, except by believing in Him - and that He would give us the ability to live a Christian life here on earth and spend eternity with Him and His Father in Heaven.
Do we fail? Certainly, and all the time. But does our God forgive us? If we've accepted Jesus as our savior, then the answer is a resounding, "Yes!"