ZDoom

I can see that there are x64 builds for ZDoom, now. From an end-user perspective, is there a difference between them and the "standard" builds?

They require a 64-bit version of Windows (XP x64 edition included). Other than that, no, there's not anything different about them. In benchmarks they may turn out to be slightly faster. If my Linux 32-bit vs 64-bit tests apply then we're talking a consistent 5% faster, but it's not anything you'll notice (that comes out to about 3fps faster). They also are compiled with Visual Studio 2013 instead of 2005.

I wouldn't mind having GZdoom 64 bit builds. However, unless you're taking advantage of the 64 bit (lets say super high resolution textures in Doom or loading a 2gb soundfont all the way via Coolsoft Virtualmidisynth) I'm not sure if there's going to be much of a use for it.

In GZDoom 64 bit will be slower, actually. The reason for this is that the GL code contains a lot of function calls which create some significant overhead with 64 bits, but on the other hand most math is floating point so 64 bit has no advantage here. GZDoom also can suffer from cache hits, and the larger pointers in 64 bit will make this worse.

The last time I tested 32 bit was approx. 10% faster.