I would say what difference does it make now.
Within The world wide Muslim community, the belief that Jesus is still to return and die, before Day of Resurrection, had become widespread. In more recent years, the belief in return of Jesus, or even the Mahdi, has been fading.
The Christians likewise, believed in return of Christ. How strong really this belief is, among Christians in our days, is unknown to me. But, my guess is, the belief in the Return, has been also fading among Christians as well.
In many respects it makes little difference whether the Christians or Muslims are right. As correctly stated by several posters on this thread we can not know with absolute certainty either way. What is important is our capacity to reflect constructively about known history and the sacred texts of the two largest world religions. We also need to be able to respectfully converse with those with very different beliefs from ourselves in our independent investigation of truth and know when to agree to disagree.