PS3/360 controller adapters?

I know they exist, but I can't find them. Furthermore, I don't know the pro's and cons too well

I've been thinking about picking up an Xbox 360 lately because I really really really want to play HD Remix, but my HRAP3 is for PS3/PC only, and those fuckers at Capcom aren't releasing HDR for PC. I'd be getting a 360 over a PS3 because most my friends play on a 360, and I'll likely just get the uber cheap model.

Now...

- What are the adaptors called?
- What are the pros/cons (I hear they can introduce input lag?)
- What would be the best brand/model to go with?

People with experience with these things are much welcomed in this thread