There is no real advantage if the UCCNC is running on 64bit computers, because it runs as a 32 bit process anyways, so it does not really matter for the UCCNC, it runs the same way on 32 and 64 bit computers.
But for new computers there can be advantages to run them with 64bit Operating Systems because the computer architectures are mostly optimised for 64bit OSes,
so the computer itself can run faster and more efficient with 64 bit systems.
And one more thing to consider is that 32bit systems can't address more than 4Gigabytes of memory, because the address bus is not wide enough to address more than that as 2^32 is only 4.29 * 10^9,
so if you have more then 4GB memory installed in your computer then your PC still can't use more than 4GB if you have a 32bit OS installed, which is not a problem for the UCCNC,
but is a waste of money if you bought all that memory.