The only time a 64-bit OS is better than 32-bit, is when the game in question supports 64-bit properly. Meaning it can utilise the 64-bit architecture and increased RAM support (32-bit limited to 3.5GB-3.7GB of RAM, 64-bit limited to 128GB of RAM). Other wise a 32-bit game will just run in 32-bit mode under a 64-bit system.
One advantage example is Crysis. If you increase the graphics on Crysis (running the 32-bit exe) to a point where Crysis needs more than +2GB of RAM, the OS wont give Crysis anymore RAM and it will use your Pagefile which can inturn cause a pausing effect when a new area in Crysis is been loaded (Moving in/out of buildings).
Running it in 64-bit i found Crysis will use upto 4GB of RAM about double what the 32-bit EXE can access.