Default 32-bit processes on 64-bit or 32-bit Windows cannot, in fact, use more than the 2 GB user-mode virtual address space that's available to them. Unless they're compiled with the LARGE_ADDRESS_AWARE flag. Then it will be 2 or 3 GB (with the /3GB boot flag) on 32-bit, and 4 GB on 64-bit Windows, respectively. Microsoft has a handy chart.
But since the 64-bit OS's total RAM can (any by any means should) be larger than 4 GB, effects like swapping out virtual memory pages, which are detrimental to overall system performance, will occur much less.