I used `git gui` for that (not sure how "native" to git is it, though), and recently switched to `gitg` for both looking at tree and committing individual lines. Can't compare them with SourceTree, though, since haven't used that.

Also, when on command-line, I recently discovered `git add -i` for interactive mode (asks you about individual hunks and lets you "split" them), and `git add -e` (lets you edit the patch however you want).