The size on disk is completely meaningless. I guess cartoony would have lesser colors, so you could save up on a few kbs I guess? That's hardly something you should choose a style over for.
If you mean size in memory, then it doesn't matter at all... That's affected by width and height of the image.
Cartoony might have less textures over realistic ones, so rendering might be a tad faster, but just like size on disk, that shouldn't be the factor deciding on your game's style.