I worked in the computer industry during the transition from 16-bit to 32-bit. The biggest difference I saw then was it allowed for more lower skilled programmers to develop highly inefficient code that required the larger address space. Some of that still holds true for the 32-bit to 64-bit transition, although the more sophisticated Operating Systems and complex, fancy graphical interfaces consume a lot more address space all by themselves. Thankfully the HW engineers have been able to keep pace with the SW engineers and improve computer speeds to make up for less efficient SW.
So one of the main advantages of moving up to 64-bit systems is there will be a larger universe of software available to use, and most 64-bit OSes will support and run software written for 32-bit as well.