PCSX2 actually tends to require a much more powerful PC than Dolphin, even though Gamecube games in general ought to be more demanding. Dolphin has developed really, really well (it's even becoming semi-reliable as a Wii emulator nowadays), but PCSX2 is still quite a way behind. It's not nearly as efficient as Dolphin.
Both are very good mind, and constantly improving. In another year or so, Gamecube and PS2 emulation could well be pretty much perfect, much like GBA emulation is now.
For reference, I've played Zelda: Twilight Princess in Dolphin, and it runs great everywhere except Hyrule field, where FPS drops to about half. Everywhere else in the game is pretty much full speed, or near enough. In PCSX2, I can only really play turn-based games such as Persona 3 and 4 (which both run perfectly). This is with a Q6700 CPU overclocked to 3Ghz, and an HD4890.