Steve, usually the biggest difference between an amp head vs. a separate preamp/power amp rig is tone: Generally, standalone heads have a certain, small amount of distortion left in them, which our ears interpret as 'warmth'. When you use power amps, since these are usually built to pro sound system specs, the distortion amounts are many, many times less, so these almost always sound a LOT cleaner. Couple this with the usually higher power ratings of these things, you have a lot more headroom, which adds to how clean they can sound.
And as you can see by Charles' rig above, you can just 'one-piece-at-a-time' it to build quite complex signal chains if desired. Or if you're needing a BIG rig, you just keep adding power amps and cabs as needed.
But it's just another choice: For some guys, they sound sterile. Or you may not want to lug around rack cases, etc. But generally it's for a cleaner tone made possible by the higher spec components, though the difference is not as obvious as it once was. In the old days when an SVT or Acoustic 360 was as big as you could get, an Alembic preamp and as many Crown amps as required was a HUGE leap forward.
J o e y
