Do any Christian scholars contrast Islamic eschatology with Christian eschatology? Are there any Christian scholars (and their works) that comment on Islamic eschatology, and/or contrast it with Christian eschatology? As an example of a Muslim scholar coming at this question from the opposite side, Imran Hosein wrote "Jerusalem In the Qu'ran", which looks at both Christian and Muslim eschatology from a Muslim perspective.
No doubt there are Christian scholars who have studied Islamic eschatology but, although I have read a small number of books on Islam, I have not read any specifically about Islamic eschatology. However, a search of the internet found at least one interesting example from Joel Richardson, with enough preview information to suggest it could be recommended to the OP for his interest. I find that Richardson is not a scholar in the usual sense of the word, but a Christian preacher and author. 

Joel Richardson (Antichrist: Islam's Awaited Messiah) speaks (page xv) of having  Muslim friends all over the world and stresses (page xviii) that 'the purpose of this book is by no means to "bash" Muslims in any way.'

Richardson says (page 22) his book is "first and foremost a study of Islamic Eschatology (end-time belief) and those specific Islamic doctrines and practices that seem to correlate in quite an astonishing way to the biblical descriptions and prophecies of the last-days." He claims (page 23) that his is the first comprehensive popular study of Islamic Eschatology as it relates to biblical eschatology.

On the one hand, Richardson sees Islam as the future of the world, but on the other hand, his theme appears apocalyptic. Islam may be the future, but the future is a dark place.