64-bit processors offer additional benefits besides high RAM capacity. For one they offer twice as many CPU registers, both SSE and general purpose, allowing for more data to be held in registers, rather than in memory. They also offer new memory addressing modes that can boost performance of linux SO libraries.
There are downside though in that code size is larger with 64-bit code, which could cause issues with code not being able to fit into caches that it could have fit into with 32-bit code. Overall a 64-bit program will run faster than a 32-bit code even with the same amount of memory.