Could Christianity and Islam ever reach a consensus in regards to Jesus' identity?
Not very likely. Or at the very least, we would have very different forms of either or both at that point.
Then again, I am not sure of how meaningful such a goal would be. For both creeds those are not really academical matters subject to research and reconsideration. For quite a few Christians and apparently nearly all Muslims the point is to proudly
reject such efforts.
If no, which of the two religions is more likely to disappear first?
Islaam, probably, since it apparently has never been a religion.
But if you mean the doctrines proper, that is not a very useful question. What would such a disappearance even be? How would we even realize that it happened?
If yes, which of the two religions do you think should and will make the bigger compromise? Will Christians accept Jesus as a divine prophet? Will Muslims adopt the concept of Trinity? Will they decide to change Jesus' status into both a prophet and The Son Of God to incorporate both beliefs?
Christians generally have no issue with acknowledging that Jesus was a divine prophet. They just tend to insist that he was so much more besides.
Muslims forbid themselves from even acknowledging that Trinitarianism deserves a word of its own, distinguishable from "idolatry", and they have also convinced themselves that such is the desire of God himself.
But that is doctrinary reality, which, to paraphrase, doesn't often survive contact with everyday reality. These matters are highly situational by nature. In Sierra Leone, at least, word has it that neither Christians nor Muslims really care all that much about those doctrinary clashes. And indeed, no one should.