In light of comments here, what is the history of the current division of tanach into pesukim? Specifically, to what extent do we view our breaks as coming from Sinai? Are there Christian influences affecting some spots? What are some places where we differ from the Christians (if any)?
Note this is about verses not chapters. Sources highly recommended.
A primary source that bears on this is Megillah 3a/Nedarim 37b, which lists פיסוק טעמים and פסוקים (the divisions of cantillation and of verses) as being of Biblical origin (דאורייתא הוא), and sees these as implied in the description of the Torah reading under Ezra's direction in Neh. 8:8.
We also have evidence from various other places in the Gemara that their verses were pretty much the same as ours. For example, ארץ חטה... ודבש (Deut. 8:8) is repeatedly spoken of as "this entire verse" in Berachos 41a, Eruvin 4a, et al. So is שמע ישראל... אחד (ibid. 6:4), in Berachos 13b; תורה צוה... יעקב (Deut. 33:4), in Sukkah 42a; and others. In Taanis 27b the sections Gen. 1:1-5 and 1:6-8 are described as being, respectively, five and three verses long, exactly as we have it; similarly in Megillah 21b the reading for Rosh Chodesh (Num. 28:1-15) is described as consisting of sections 8, 2, and 5 verses long, again exactly matching our divisions.
To be sure, there are some cases, as with other aspects of the Oral Torah, where there are variant opinions. Kiddushin 30a thus mentions that Ex. 19:9 was divided "in the West" (Eretz Yisrael) into three verses, where the Babylonians had it as one (as we do); the next line then gives the number of verses in the Torah as 5888, as compared to our 5846 (although it is worth noting that this is still an agreement of over 99%). There are a couple of places in the Torah where even today there exist different traditions on how to read them, such as Gen. 35:22 and the two repetitions of the Ten Commandments, where two sets of trop are printed, representing two different ways of dividing the verses. I guess it's conceivable that there might be places where the non-Jewish verse divisions* were taken over into our mesorah, but based on all of the above it would seem that these would be at best isolated cases.
* Not to be confused with the chapter divisions and verse numeration, which are unquestionably of Christian origin.
In terms of places where we differ from the Christian version, compare how the two of us count the introductory phrases in Psalms:
