It's amazing that none of the learned aero engineers and fliers posting in this thread mentioned the primary difference between inside and outside loops.

It's GRAVITY!

There are aerodynamics involved, as Ben pointed out. When a plane "rolls" out of an inverted maneuver, it's actually a high-speed stall, or "tip stall," caused by too great a load (G) and too high an angle of attack.

My M2-E would do that at the bottom of an outside loop, and I was able to eliminate it by mixing flaps with elevator, so that when down elevator is applied the flaps go up. When the plane is at the bottom of an outside loop, the flaps are increasing the camber in the right direction, and sufficient lift is created to complete the loop.

Here's a quiz: The record for simultaneous outside loops was held for a long time by a gentleman in a Great Lakes biplane. For the grand prize, name the pilot, and the number of loops he did.