Furthermore, if you believe the rule about weight lost to dieting coming back in five years, it seems likely that would happen to both groups. Intriguingly, though, while participants on the Mediterranean diet didn't initially lose as much weight as those on the low-carb diet, the weight regain didn't seem to happen as much on the Mediterranean diet. That makes me wonder what a five-year study of the Mediterranean diet would find.

https://en.wikipedia.org/wiki/Mediterranean_diet#Medical_research (doesn't mention long-term effect on weight, but only on diabetes and other disease; it also mentions that in the study you cited 86% of participants were men, and the women lost more weight on the Mediterranean diet than on the low-carb one).