Here's a test, have you ever tried to play Super Mario World with a 360 controller? How about Mike Tyson's Punch-Out, or Mega-Man? The D-Pad is useless, the buttons are way too fat and heavy giving too much feedback once depressed and generally have slow action. So to me, difficult platformers are much better on the PS3 controller.
Fighting games are a given in all respects.
jRPGs are games that are usually played hours on end. The lightweight SixAxis controller can be used and the analog stick has fairly little resistance allowing for extended game play. Games that have reconfigurable controls, or when playing on the PC, can be easily played single-handedly. I used to play Suikoden and Final Fantasy with one hand. Hell I can beat most people in Street Fighter single-handed on a PS3 controller.
For racing games, I much prefer the leveled and smooth analog sticks to the 360's staggered sticks. I've played Gran Turismo and Forza at length on both platforms, and without comparing the games themselves, I feel far more comfortable with the PS3 controller. Now, I'm sure much of that has to do with the fact that I've played every Gran Turismo to completion and I'm comfortable with the controls, but perhaps all this is really pretty subjective.
Suffice it to say, I think the 360 controller is really best for games where the primary mode of action is the dual analog layout with the triggers. Games requiring fast button presses would benefit from the SixAxis/DShock layout and style. Games requiring a D-Pad shouldn't be played on the 360 controller, which is a big issue for 2D games, platformers, menu driven games, and fighters.
Depends on what feel you're going for. I'd agree if I'm playing Halo. I'd be upset if playing Tekken.
DS3, to me, isn't light at all. The SixAxis is light, even somewhat flimsy. But they serve different purposes. I'd rather play with a SixAxis for all genres save racing, and for that I'd prefer the DS3. For a FPS I just the the PS3 controller isn't well suited, and since that's the primary genre today, I can understand why people don't care for the PS3 controller. If most of what you play is FPS, then you'd probably be better off with a 360 controller..