I am aware of some the obvious gains of the x64 architecture (higher addressable RAM addresses, etc)... but:
One issue to keep in mind is the software libraries available. For instance, my company develops an application that uses multiple OpenGL libraries, and we do so on the OpenSuSE OS. In older versions of the OS, one could download a 32-bit versions of these libraries on the x86_64 architecture. Newer versions, however, don't have this. It made it easier to just compile in 64-bit mode.