We had dinner at both places during out last trip in September '06, and we enjoyed them both. I think the service we got a CM's was better. At CP there is no picture package, so there is one less distraction (and expense) at dinner. CM's was quite loud, but my kids were contributing to that so I couldn't complain. They got a big kick out of watching the monorail entering the Contemporary.
Character interaction was good at both places.
A good point another poster made. You do not need a park admission to go to CM's!!