Christians actually have variants whilst Muslims have Multiple Readings. Muslims are meant to have multiple Readings of the Quran as per the way the Quran was Revealed. Christians are not meant to have variants. Because they have variants they need Textual Criticism (to speculate which MS reading is the original) and continuous archeology (to continually look for new MSS to help them find new variants or to find evidence which helps them speculate the strength and veracity of various readings already in the NT MS tradition). In addition, the Bible is a text still in flux, in that any verse could be relegated to a the status of a later addition (i.e. forgery) upon a new manuscript find – the historical precedent was set quite spectacularly for this in the 19th Century with Dr Von Tischendorf’s find (or theft :)) of Codex Sinaiticus (relegating the PA and the ending of Mark to the status of later additions). In fact the Christians have given up the keys to the Bible to the academy now.
Qur'an Seminar 2017: Learn about Quranic Preservation
Facts About Birmingham Quranic Manuscript Discovery - Louay Fatoohi