I believe it can be more or less proved, or at least there is better evidence for the truth of the Bible than the Gita. First off let me state that the philosophy of the Gita makes more sense to me on a rational level than that of the Bible, and yet I believe in the message of Jesus. Just because something is rational or seems sensible or can be explained convincingly, doesn't mean it is necessarily true!

The evidence of the Bible comes from the multiple testimony of people who witnessed a man who came not just with words of wisdom, but was witnessed performing a crescendo of astonishing, effortless miracles culminating in raising himself from the dead, as he had said he would! The witnesses held on to their testimony for all their lives in the face of serious persecution. Most of them were killed for that testimony.

Another piece of evidence comes from the fact that the coming of Jesus was foretold in the writings of the Old Testament, which is dated to well before the birth of Christ.

As for the Bhagavad Gita, tradition has named an author for it, but there are no independent witnesses testifying soberly to the miracles of Krishna. In fact it is only a part of a much larger epic, the Mahabharata, which seems a legend much like Homer's Odyssey.