The advantage of a 64bit version would probably be no longer running the game via Windows On Windows (WOW64), which all 32bit processes run under when used on a 64bit version of Windows. Technically WOW64 has some overhead versus a process running naively. Realistically the overhead is so small it's not a concern and run as well as if being run on a 32bit version of Windows.

The "PS3 version's is to blame" excuse is a complete red herring. It's a completely different platform, running a completely different build. It would be like for me to say your old Android phone is holding back my new iPhone. It's silly and completely untrue, and should be regarded for what it is. Utter nonsense.