Most accurate emulators for each system? MESS included

I'm looking to run old games accurately.

Also, I have an fat PS3, one of the 1st that came out. I hard these run PS2 games better than the slim ones. So would it be better to jailbreak it to run all my games?

When you mean for each system, do you mean your consoles? So far I only have good knowledge on emulators for the PC.

yep, I mean consoles