Separate preamp, power amp, cab rigs are quite common. I use a clone of an Alembic F2B preamp that I built myself, a QSC Powerlight power amp and an EV TL606 cab. Soon to be replaced with an Emi 3015LF / B&C 6PEV13 cab. I love the sound of my rig and I'm sure I'll love it even more once I get my new cab finished.
The pros are that they are very flexible rigs. You can use different preamps and different cabs as the need arises. The cons are that it can be quite expensive and it seems to exhibit a kind of "big rig" attitude that sound guys look down their noses at. "Oh crap, here comes another bassist with a big rig." Just make sure that whatever preamp you choose can properly supply enough juice to the poweramp you will be using. Different preamps have different levels of output, and some poweramps are more sensitive than others. I have no problem driving my QSC with my preamp, they match well.