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/
| Parameter | Description |
|---|---|
| -u | Unified diff |
| -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) |
| ./repo_dir/ | Unmodified |
| ./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/