Aphex's process is different than the BBE processor, but they do wizmo gizmo stuff to the sound that usually boils down to (as hungovermorning stated) harmonic augmentation at specific frequencies, sometimes program dependent, and I don't know about the Aphex unit but the BBE processor phase-aligns source material accross the frequency spectrum...My 462 has two controls, one for "Process" and one for low-frequency. IIRC the "Process" knob is mostly the phase-alignment circuit and the LF knob is a harmonic enhancer...
I use my 462 in different ways...sometimes it is handy when remastering live material. I really like what it does but I've learned to use it sparingly unless I'm using it as a multi-effect...using the LF enhancer to get really fat distorted kick drum sounds in conjunction with other processors. I also have used it as an insert along with a compressor on my electric bass. Its an old Ibanez Roadstar II...the neck has some stability issues so the intonation is funny sometimes, but it is a passive bass with two soapbar pickups that are individually switchable humbucking or single-coil on push-pots...three knobs total: one volume, one tone and one fader between the two pickups...anyway, with those two processors I've been really happy with sounds I've gotten recording direct without any sort of schmancy preamp...just a hi-z input with the 462 and compressor inserted.
Anyway, there's my 2p.
I've heard lots of people that prefer the Aphex exciters to the BBE. Different process but harder to overdo, and Aphex (IMO) makes quality rugged stuff for the professional environment.