I assume you're talking about a rack setup (although you can get some amp heads rack mounted- some of the Mesa amps have rack ears that can be attatched, and quite a lot of bass amps do too).
Pro's:
-Cooler :)
-More customizable tone due to it being modular
-Easily expanded
-'Easily' maintained (just replace a certain unit rather than the whole thing)
Con's:
-Harder to find 'the' tone due to more options
-Can get more expensive
-Bit of a pain to lug around
The most basic of rack setups would be:
Preamp (example: ADA MP-1)
Poweramp (example: Mesa 20/20)
Rack tube poweramps are pretty expensive, but if you choose wisely, you can have a true stereo setup, and have one cab on each side of the stage(or each side of the bedroom/lounge), for really nice chorus sounds and ping-pong delays :)
Personally, i keep switching from my rack setup (a little complicated) to my JCM900 setup (guitar > overdrive > amp), i find both to be great, but i don't fancy dragging the rack stuff to a gig :)