If you assume it's consistent within the list (either {10} or {13,10} or {13} for every line ending), then something like
In[103]:= Max[Count[bytes, 10], Count[bytes, 13]]
Out[103]= 2
is probably pretty efficient. If you want to support a mix and match, something like this should work:
In[104]:= StringCount[FromCharacterCode[bytes], RegularExpression["\r\n?|\n"]]
Out[104]= 2
Count[bytes, PatternSequence[13,10]] doesn't work because Count doesn't support sequence matching, only element matching. To do that kind of thing for Mathematica expression, one typical approach is
In[109]:= Count[Partition[bytes, 2, 1, 1], {13, 10}]
Out[109]= 2
but it's not very efficient (and wouldn't cover the other cases anyway).