Basically, the Christian missionaries' argument is circular. According to them, the Bible says such-and-such and the Qur'ân says such-and-such; therefore it follows that it is a contradiction in the Qur'ân. Since the Bible says so, it must be true. Proof is not necessary, Belief is sufficient.
No attempt is made by the Christian missionaries to show that the Biblical account is historical and the Qur'ânic one a legend.