Active mode works to eliminate stronger, higher frequency vibrations. Panning detection is disabled while in this mode. It tries to damp *all* motion.
Normal mode is looking to eliminate the kind of movements you make while hand-holding. These are generally lower in frequency. It also attempts to automatically detect panning motions, at which time it disables horizontal damping action.
I guess it depends on the aircraft. If it's a 747, normal mode will probably be enough. In a Cessna, you might want to consider active mode. Go figure...