Personally, I don't believe the whole 'eat more to lose' moto. I don't believe it's common for dieters to hit starvation mode either (I've read a lot of articles pulling both ways, and from what I've concluded is that, say, if you lose 2lbs a week on 1200 calories and decide to cut down to 700 calories... you'd EXPECT to lose 3lbs a week, but in reality it turns out to be 2.5. You still lose, and you still lose more, but at what point is it not worth eating so little?)
With that said, I do feel that eating more as opposed to less is best. Not because you'll lose more, but because it's more manageable. If you did go on eating 700 calories, you'd lose a lot! But in no way would it be healthy. Furthermore, eventually you'll want to cut your calories a bit more to help escape a plateau, and if you're down at 700 calories, or even 1200, cutting is not going to be fun!!
As far as burning vs starving... I side for the burning
I don't think you'd lose MORE since it's so much easier to have a small pastry than to run on the 'mill for an our, however by exercising, your body reshapes, and it looks like you've lost more, even if that's not the case.
I also think you're appetite will go down as your tummy shrinks. My boyfriend, who has lost a bunch of weight (without even trying to!!!! GRRR!!!
) cannot eat nearly as much as he used to be able to wolf down. But, don't starve yourself! Maybe you should eat more protein and less carbs to feel more full?