You can't play emulators and homebrew on a 360 -- you can only play "backups." Playing on live with a modded system is an iffy proposition though, and may get you banned.
The PS3 "scene" is pretty much nonexistent. No hacks, no mods, no backups, no homebrew. You can install linux on a PS3, but it doesn't give you any nice features games-wise, just lets you dual boot between PS3 and a linux box.
I agree with Haruman, if you want to play emulators, get a modded Xbox 1. If you want to play online with real games, get 360. Live is FAR superior to the PS3 online system, and you can find it on sale for $30-40 for a year, and it's worth every penny.