You can somewhat improve the situation if you adopt a somewhat weird source-formatting policy, where you write each sentence on one separate long-ish line, rather than flowing by paragraph. Then you will be able to automatically merge as long as nobody has made an edit or move that touches the same sentence, giving you better merge granularity. But even then conflicts happen pretty often, and few people like this style of formatting (maybe it'd work better with tool support).
For a book this might work better, though, because I assume you'd be making less frequent edits, and people would less often be working at the same time.
As stated above, Dropbox doesn't even try to merge files, but Git does, which is definitely an advantage (at the very least, it tells you where the conflicts are, which is far more reliable than trying to work out the conflicts by hand, or with a separate diffing tool).