The AM is the closest BK to the 81, quite easily.
They dont sound *terribly* alike, but the AM is the closest relation to the character of an 81 in the BK range: the AM has a more open, 'chimey', high mid and top end that lets dynamics through, is a little more blurred in the low mids and low end, is similarly middy, but the mids have a somewhat grindier character, its noticably but not cripplingly lower output, but louder and generally less compressed as well.
Basically the aftermath is a little looser, little cooler, but more dynamic and open, chimier and fatter/bigger sounding. And, I've had both pickups in the same guitars, and in different ones in A/Bs.
The MM has a similar inyourface high mid to the 81, but its low mids are quite a lot bigger and chunkier, and its also not as hot, and lacks the foward mids of the 81 in *most* guitars. Very gutiar sensitive pickup, as with all BKs, where the 81 is quite a bit less so, so I can see how in certain guitars people would hear similarities, but after having both in quite a lot of guitars the AM is the closer relation (followed by the painkiller).