Again, how so? Neither Koran nor Bible demonstrate the existence of any God in my opinion. So which one do I go with and why?
Pick a recipe you like and follow it. Read the shopping list of things required, and go out and buy them, and do what it directs. Then later you can throw away the list if you want to as you enjoy the nourishment.
Have you read the Bible and the Koran? If not, you need to do so. Then I'll be happy to reply to specific follow up questions. Finding truth does take effort, especially on a topic as deep as God.
Now you are switching the subject. The question is not whether Bible or Koran can "demonstrate the existence of any God" to a skeptic, but if content of Koran is in sufficient agreement with the Bible to consider God of Abraham, Isaac and Jacob as God of Muhammad.
Go to the library and do your homework, son.
The apostle Paul, in Romans 1:19-20, indicates that the existence of God may be deduced from the observation of nature. The approach that many Christian apologists, such as Thomas Aquinas, have taken in this matter is to use evidence of orderliness in the universe, benevolence toward humans and other life on this planet, etc., to point out the absurdity of not believing in the existence of God.
But of course, all that these arguments support is the improbability of the universe being organized via random chance. It does not prove the claims made by the Bible of God's character, His Triune nature, or the unique role of Jesus Christ. That comes from accepting the Bible as true because it is God's Word and thus reliable in these matters.