I would do both but you could make a conscious effort to feel the back muscles during chins/pullups. I try to do them the way Milos described them; do as many chins as possible using your lats to pull you up and then when your lats start to fail you start using your delts and arms. Believe me this is possible and you continue to get stronger. Try this workout for pullups. It will get you stronger.
1, 2, 3, 4, 5, 4, 3, 2, 1 reps
Do that. When you can do that go up to 6, then 7, etc and pyramid back down. If you can go up to 10 you should be able to do 20 strict dead hang pullups.