Focusing the sound captured on a narrower area is the strength of shotgun mics, and, in general, the longer the mic, the farther the distance, based on what I've read.
Again, it depends on what OP's trying to do, location, kind of shot/group, and the distances involved. The narrower field does not stop when it gets to the intended source, is one thing to recognize, so if there's noise behind the source/group, it's going to get picked up as well, unless it's much quieter than what the intended source is. Some of the mics have a hypercardioid pattern as well, so there's the possibility of noise entering from behind the mic.
And, those shotguns that have AA batteries are longer because of the battery length - i.e., that length is not comparable to a battery-less model that's just as long!