Depends on my mood. Sometimes all I want is a shallow character, a simple story and the fun and games that go along with it. I typically prefer to focus more upon my character but I still like my mechanics.
I suppose that I'm really in the middle. If a game becomes to much of a 'pass the stick' then I lose interest because frankly we all may as well spend less effort to do it. Too much emphasis on the mechanics and soon the characters are just sheets of paper with stats.