If you are going to game on a decent HDTV and sit down some distance away on the sofa, then to most eyes, there will be little difference. Resolution junkies (I prefer high res if I can get it) will prefer to get the PC version, and run it at 1920x1200 or even 2560x1600. This high resolution allows you to sit closer to the screen (more immersive IMO), and still not suffer from screen door effect or visible pixels.
As pointed out, sometimes perfect clarity can show up games as being a little bit behind, so in some cases you can argue that the fuzzy vaseline-smeared-lens look of a 640p (Halo 3) console game upscaled onto a 1080p display (plus LOADS of bloom) covers up these defects.
PS3 versus PC. If you have $600 you can get a PC that is significantly more powerful, what with the ridiculously low price of the 8800GT now. Hook said PC up to a 1440x900 monitor, or if you prefer, a 720p HDTV (easy to run games at that low a resolution), and you are laughing.
However, if you want to play Crysis on Very High (one of the few games out there that shows the disparity in PC/Console hardware) at 1080p or higher, then I would recommend the bare minimum of 4850, but ideally a 4870 or better.
A good gaming PC still costs more than a PS3, even using good value parts (8800GT, E4500), but if you are going to use it a lot it will be worth it.
Also, if you are a sad nerdy loser like me, the PC opens up many more crazy options. My triplehead gaming setup