Using the diff tool (utility, whatever) I got exactly what I wanted: a unified diff file of all the files in a directory (recursively) including newly added files, but not removed files and some other pesky files.
Here is the command I used:
diff -u -r -x '*.meta' --unidirectional-new-file ./repo_dir/ ./exported_dir/
|-r||Recursively traverse the directory|
|-x '*.meta'||Ignore all files ending in .meta (For Unity3D's "repo friendly-ness")|
|--unidirectional-new-file||Include new files in the diff, but not removed ones (for that use -N)|
|./exported_dir/||Contains modified files|
Diff's help and man pages are pretty sparse, the online manual is much better: http://www.gnu.org/software/diffutils/manual/