Pixar has made more great films, but Aardman is brilliant as far as straight-up comedies go (its when it comes to being forced into stories they become second-rate).
It's a tricky one - Aardman never really did anything as influential as Toy Story, but I'd say they're a little more versatile than Pixar. Their work in short films and advertising is pretty diverse.
I think one hurdle for Aardman is that most of their stuff now uses Nick Park's style of character design. Unless you see the less mainstream stuff like Angry Kid.