100% of 64-bit computers run 32-bit programs. The vast majority of users never know or care what arch is installed. The only time most people care about bit-ness (word?) is if they are 64-bit trying to run an ancient 16-bit program.
This isn't VHS vs Bluray; it's much harder to explain why there is an advantage when it can't be seen. The 64 not version isn't 35% faster, or has dozens of new features. It's mainly just compiled differently, and it is hard to explain memory limits and instruction sets to people.
But, does a program can use more than 4GB of RAM if it's compiled in 32-bit and executed into a 64-bit environnement (with more than 4GB of memory)?
I imagine that the answer is between yes and no.
I imagine that you, as developer, can choose between limiting your program not to use more than 4GB or let the system (host) do the memory re-mapping job for you...