You can't out-train a bad diet. (And you certainly can't out-situp one.) Absent a Tour de France-competitor level of activity, fat loss is a function of diet, not exercise.
To lose fat, you'll have to average a significant caloric deficit for a significant amount of time. In my opinion, a good starting point is to run a 3500 cal/week (500 cal/d) deficit, which translates into losing about 1lb/week. As to how you elect to create that deficit (eg, via carb cycling; Atkins; IF; etc), that is largely a matter of personal preference.