With 4GB and Windows 32-bit, you'll probably have no more than 3.25GB actually available to you. With 64-bit you would see the full 4GB. That's advantage #1.
#2 is that applications running under 64-bit are assigned a virtual address space of 4GB each, whereas in 32-bit they're limited to 2GB (unless you use the /increaseuserva option in bcdedit). (Note: such programs must be LAA aware, that is, compiled with the "large address aware" bit set on.)
For demanding apps this can be a real boon as they won't crash or otherwise bomb out if they need more than 2GB.