In terms of comparing authenticity between the Bible and the Quran, there is no comparison.
**Similarities: **
The Gospels of Jesus were not written by him.
The Quran of Prophet Muhammad was not written by him.
It being compiled by the disciples or companions of the receivers (Jesus or Prophet Muhammad), the disciples or companions are considered upright and trustworthy. Therefore their compilations are to be trusted.
Differences
The Quran was compiled by the Disciples or Companions of Prophet Muhammad, (Verifiable). No Muslim scholar differ about this fact.
2 of the Gospels (Matthew and John) of Jesus was allegedly compiled by the Disciples of Jesus. I say allegedly, because Christian scholars differ about it.
The Gospel of Mark and Luke, were not written by the disciples of Jesus. So need to discuss these two. Not to say there aren’t relevant.
Corruption
If we were assume the Gospels of Jesus were originally written by the disciples of Jesus, there is evidence that those who came after them, corrupted the Gospels. For example, John 8:1-11 In the early manuscripts this can be found anywhere, yet it exist in later copies of the Gospel of John. This is a deliberate addition or corruption. So knows what else was added by those who came after the disciples of Jesus. However Christian scholars agree that things were added to the Gospels.
This does not exist in the Quran, by scholarly Islamic consensus.
Conclusion
The Quran can be authentically proven to be from the disciples of Prophet Muhammad by scholarly consensus, by those who believe in it.
While the Gospels, no scholarly consensus exist with regard to the authors among those who believe in it. Some say it was written by the disciples, while others questions it.