One place where non-Jewish editions break a verse differently is in Sh'mot 20 (ours, theirs). We read the following as one verse; they break after מִבֵּית עֲבָדִים:
אָנֹכִי יְהוָה אֱלֹהֶיךָ, אֲשֶׁר הוֹצֵאתִיךָ מֵאֶרֶץ מִצְרַיִם מִבֵּית עֲבָדִים: לֹא-יִהְיֶה לְךָ אֱלֹהִים אֲחֵרִים, עַל-פָּנָי.
Some chumashim break this into two verses too, but this appears to be an error, possibly arising from Menachem Lonzano's work. It appears that all the manuscript evidence which we now have disputes this division. For example, this manuscript shows it clearly as one verse (see this image). Further, the mesorah at the end of Sh'mot counts 1209 verses, but if you count with this division, you get 1210. I am indebted to @DoubleAA for the information in this paragraph.
There are lots of off-by-one differences between our and their counts. Most of the differences listed in this article are of this type. For example, in Tehillim Christian editions tend not to count the incipit as a numbered verse, causing everything else to shift. For just one example of this, 41 has 14 verses in Jewish editions but 13 in non-Jewish ones.