+1, in code the basic unit is usually a line, but in prose it is the sentence. I've tried using git with LaTeX and it always ended up with weird situations where you had to put each sentence on a different line to make it work effectively.
It's the diff-viewing infrastructure that needs to be completely replaced for prose.
I think you're right: if the diff-viewing infrastructure was abstracted (plugin?) it could do this and more (eg word-diff-by-paragraph, image-diff).