It is my understanding that FatBoy pickups only come in the AXY shell.
A standard AXY and an MXY sound the same because essentially they are the same except for the shell. The larger shell of an AXY looks more appropriate on some body shapes, and the thinner MXY looks more appropriate on others.
Thus, the magnet in both is the same.
A FatBoy pickup is an AXY shell with a much wider magnet. I believe it is approximately twice as wide as the standard AXY/MXY magnet. Wider here means the distance from the edge of the shell facing the neck and the edge facing the bridge.
Thus, being wider along the length of the string, the magnet in a FatBoy sees more of the vibrations of the string.
When a string vibrates it essentially forms waves; thus, as a generalization, the longer a section of string a pickup sees, the more variation in the wave it sees; and the shorter a section that it sees, the less variation in the wave.
Thus, as a generalization, the thinner the magnet, along the length of the string, the cleaner the sound; and the wider the magnet, the dirtier the sound.
So, a FatBoy sounds dirtier than a standard AXY (or an MXY). And dirtier means less clean, since the FatBoy is seeing more variation in the wave at a given moment in time. Thus in a given moment of time the picture of the wave form is not as clean.
This is what I understand to be the difference in these pickups. I've never owned a bass with FatBoys; all of my basses have either had Series pickups, MXY's, or standard AXY's. So I am not speaking from first hand experience.
My guess, and it's only a guess, is that given the types of music you play, you would probably not want a FatBoy in the neck position.
I hope that helps.
