I definitely prefer it when the Muppets play themselves. There would seem to be so many more stories that could be told about the Muppets just being Muppets. To me the original trilogy included the best movies, and they're the only ones I'm willing to watch over and over. It's not necessarily that I disliked movies like MCC and MTI, it's just that to me these weren't really Muppet movies, but were really just movies including the Muppets. That being said, I hated MFS, in which the Muppets did play themselves. To me the Muppets just lost something intangible after those original three movies, and I don't know that they can ever get it back.
To me there was just never another TMM. Even the other two movies in that "trilogy" fell short of that amazing first film. So definitely, just let them be themselves, at least once in a while.