Cthulhu is ONLY PlayStation 3.
Multi-Console Cthulhu is ONLY PlayStation 3, PlayStation 2, PlayStation, GameCube, SNES, NES, and more.
ChImp is ONLY PlayStation 3.
None of the above have Xbox 360, so you are wrong that the Cthulhu is PlayStation 3 and Xbox 360.
The only PCB that has both PlayStation 3 and Xbox 360 is the Datel/Paewang.
With any of the Cthulhu and ChImp, to get Xbox 360 will need Xbox 360 Controller for Dual Mod.
You can do a Triple Mod with ChImp and Xbox 360 Controller and PlayStation Controller if you want.
Or just use a Multi-Console Cthulhu for PlayStation 3 and PlayStation 2, then Dual Mod that with Xbox 360 Controller.