I own both, so listen up:
PSX: Arguably the best console ever made, not because of the hardware, but because of the games. Oh, the games. Best console games ever are for this system. They're also cheap, and the you can't argue with portable hardware, soon with car adapter and LCD screen. Yum.
Dreamcast: Superior Graphics to PSX (and so far, to the PS2 as well teehee), and online gaming is a treat. A lot of great PSX ports are coming to dreamcast in one form or another, also a lot of great PC games. The games are more expensive for the most part. And, of course, since the system is kinda dying (by that I mean it's stopping production) there's always the risk that it could die off eventually.
So, it's a matter of your priorities. I say get both if you can afford it.