We did a study in the mid 1980's comparing an ACT protocol for weight control with a "best of breed" CBT protocol in a 12 session group format. The results were pretty good for both of the interventions, but not different. This was early in the research program. Self as context, contact with the present moment, and values were all less emphasized than they are now. I have no idea though if a more modern version would be more helpful.
Frankly I'm skeptical.
But others are now trying it again, so we shall soon see.
Steve Hayes