Update for Git v2.2 onwards:
git stash list --stat works.
Things have changed since the question was asked and OP’s dilemma no longer applies. From Git v2.2 onwards, you can simply pass --stat to git stash list and it will behave as intuitively expected.
You can also use any of the other file listing options such as --name-status, --name-only and --raw available to git log.
The original answer below applies if you’re using a version of Git prior to v2.2.
Original answer:
Like this I guess:
git stash list | while IFS=: read STASH ETC; do echo "$STASH: $ETC"; git diff --stat $STASH~..$STASH --; done
(Tested in Git Bash msysgit.)
git stash show $STASH instead of git diff --stat $STASH~..$STASH also worked but was unbearably slow.