There is literally zero historical validity to the Islamic claims about Jesus, whereas the Christian claims are historically sound and fit in with all the available evidence. What's more, Christianity's origins are well-documented and fully reasonable based on the reported circumstances, as opposed to the beginnings of Islam which are shrouded in a weird fog, resulting in many historical challenges and gaps in the textual and archæological record.
I would also posit all the miracles and strange events over the centuries as good proof of the reality of Christianity (e.g., stigmatists, Marian apparitions, visions of Christ, etc.), whereas those kinds of things are rarely if ever reported (let alone in a trustworthy fashion) in Islam.
Faith and personal experience also come into it, naturally. But I came to Christianity via the intellect. Comparing the claims of and evidence for Christianity and Islam, even when I was an atheist, was no contest at all: the former is far more believable and well-attested to.
Also, most Muslims who I've seen discuss these issues (as well as theology in general) are complete brainlets by European Christian (e.g. Ss. Aquinas, Augustine, etc.) standards.