Bigger in front usually is for better cornering traction, while a smaller rear makes pedaling a little easier. Everyone's tire set ups are personal preference, just like a seat. There really is no rule of thumb, run what works for you.
Correct me if im wrong, But I think that running skinny tires would be better on smoother trails. And a fatter tire for rocky and muddy trails. That way you absorb the bouncing on rocks with the extra tire area touching the ground. And also with skinnyer tires would have less rolling resistance.
I run a Specialized FastTracks 2.0 in the rear and a Spec. Roll-x 2.0 up front. They're both folding, aarmid bead so they're pretty light. The rear has pretty low knobs and rolls super quick, and the front is a bit more aggressive, to make up for the lack of width, and works great in looser soil and on roots. I run smaller tires because I commute on this bike as well as ride trails, so it really helps to keep the rolling resistance to a minimum. I keep them at 76 psi. around New Brunswick, and drop them to 38 once I reach the trail. Has been working pretty well for me.