A Muslim would first point out that his revelation is more current than yours by seven centuries - that he has the benefit of an program update from God that you missed. I would note this is essentially the same argument with which we Christians confront Jews. Secondly, he would fully agree that the guidance provided by Jesus is essential in leading a life that would be rewarded by God. After all, Jesus is recognized as the greatest prophet before Mohammed. Finally, we have no comment on Islam form John, because it did not yet exist.
The most damning issue with Islam is the conflict between internal critique and appeal to external authority.
In the Quran, it spells out clear as day that the Injeel (New Testament) and the Torah/Tanakh are valid, authoritative scripture. That's not my words, that's the Muslim's prophets words as laid down in the Quran which they believe is A.) Eternal, B.) Always did exist, C.) is uncorrupted, D.) and lays down the perfect final example of how to live for all time.
So the internal authority in the Quran points to the above and also states that the OT and NT are authoritative.
So best case of logic: A.) The Torah is True, B.) The New Testament is True, C.) The Quran is True. That is the burden of Islam to prove.
However, there are numerous conficts between the Bible and the Quran that cannot be reconciled. So either the OT and NT are false, or the Quran is false, or all of them are False. This is the Muslim dilemma.
Most mainstream Muslims contend with this damning connundrum by stating that the Old and New Testaments have been altered and contaminated. The problem with this assertion is that A.) We have all the manuscripts that far predate the era of Mohammad, so we know exactly what 7th century Jews and Christians believed and what they read. B.) The assertions by Mohammad as to what Christians and Jews believe was not accurate for the 7th century, such as the Trinity is the Father, Mother, and Jesus. C.) There is no evidence for a "uncorrupted" version of the OT and NT that can be presented that would give an alternative scriptural translation that could have been known to Mohammad in the 7th century.
Numerous examples exist of this conflict in the Quran versus the Bible, including:
A.) divinity of the Messiah / Christ, that Allah has no son yet the Messiah is his son in the OT and Jesus is the Son in the NT.
B.) Description of heaven being hot with need for shady and cold water in the Quran, versus it being in no way described that way in the Bible.
C.) Salvation and knowing salvation.
D.) Kosher laws are authoritative in Islam, yet the prophet eats rabbits and camels.
E.) That you should only pray to God, yet the daily islamic prayers invoke Mohammad.
In short, only two options remain: either A.) OT and NT are false, making Islam false, or B.) alternatively that the OT and NT are true, therefore Islam is false.