There are several concepts in the New Testament that differ with those in the Quran. Muslims revere Jesus as a great prophet, but do not consider Him God. Muhammad taught that Jesus was not crucified, but was taken to heaven-and a substitute appeared to die in His place (Sura 4:157). This is strikingly similar to some Gnostic teachings Muhammad would have encountered in his travels.
The Quran affirms Christ's virgin birth, but in doing so appears to confuse the identities of Miriam, the sister of Moses, and Mary the mother of Jesus. In Sura 19:28, Christ's mother is called the "sister of Aaron"a phrase which everywhere else in the Quran refers to Miriam. In response, Muslims suggest that "sister of Aaron" is a generic term meaning "virtuous woman" even though such a usage occurs nowhere else in the Quran.
Depending upon which Christian and Muslim sect you are discussing, the Quran teaches the 'immortal soul' which is unscriptural and Hellenistic in origins. Muslims believe in a vengeful God who tortures souls in fire continually by giving them new skin as soon as the old is consumed. The rewards for some are multiple virgin women versus the New Testaments death is akin to sleeping and all who repent and accept Jesus after the Judgement become sons and daughters or co-equals in the God Family which will come to Earth (Rev. 21).
The Shia branch believes the 'Mahdi' will come to cause World War and destruction in order to enter the new world. The NT teaches the 2nd Coming of Jesus to put an end to World War and establish the Kingdom of God on Earth.
There are other differences between the two.