Not a whole lot in the grand scheme of things. A smaller body will give more instant response in low rpm. A larger one takes a bit more to really get flowing and will favour top end.
The fueling requirements do change though as the engine is essentially an air pump pulling fuel through the carb. Pulling the same amount of air through a smaller opening will increase velocity and as such pull more fuel with it, thus requiring smaller jets to supply the engine with the same amount of fuel.