I'd say that the easiest thing to do would be to modify the source to diff to make its quiet output actually quiet. It's a little wordy now. If you just wanted to solve it for this one problem, it should be pretty easy to just edit out the talkiness. It shouldn't be a lot harder to modify it to make a new option.

Anyway, once you did that you could come up with a one liner. Something like ``newdiff --actually-quiet --recursive --brief | (cd newdir ; xargs tar cf dirdiffs.tar )''