I cant say I do Pilates but I do core training and strength training. One advantage of strength training is something called excess post-exercise oxygen consumption. I am not a doctor or exercise physiologist so this might be a bit non-scientific but I do read a lot so here goes.
When you lift weights you raiser your heart rate, elevate your caloric expenditure, and damage muscle fibers. Your body needs to then repair those muscle fibers (making you stronger and the muscles grow) which uses energy in the forms of calories.
Also keep in mind the metabolic benefit of losing fat and gaining lean muscle. It takes more calories to support one pound of muscle than it does one pound of fat. The actual number vary a lot but even the lowest case scenario I have seen states it takes approximately 3 times the calories to support a pound of muscle than a pound of fat.
One more thing to think about if you are dieting is that all the weight you lose wont be fat. In fact it is easier for the body to shed muscle than fat. This is an evolutionary problem that comes from when we used to hunt and gather instead of head to the supermarket. If you only diet and dont do any sort of muscle building activity you may be losing muscle along with fat and that isnt good.
I recommend doing as many different kinds of cross training as you can. This could be Pilates, weight training, biking, kayaking, climbing, snow-shoeing, and of course walking/jogging/running. I wouldnt look at it in an either-or scenario, the more varied the better.