I use XP64 on my main PC. I haven't run into any problems with it, it works just as well as XP32 does. I have a dual boot with XP32 but I haven't had any need to fall back on that at all and wouldn't mind deleting it at this point. I like XP, but I don't see the point of running the x86 version if the system supports x64 and it works just as well. 😀
Unless you're trying to use a really specialized or anachronistic piece of hardware then finding drivers shouldn't be any problem. As far as I've been able to tell, any mass market device that was supported during the life of XP64/2k3 has drivers for it.
I haven't run into any XP32 software that breaks on XP64, but I'm aware that old 16-bit apps/installers aren't going to work. I would assume that anything affected by the 16bit issue falls into the stated category of "runs fine on a P3 with Win98".
Programs that have an x64 version can potentially run faster and it can access GPT drives, though sadly it can't boot from them.
The only strange thing I've run into is that for some reason, on XP64 the tooltips for the taskbar icons are very prone to dropping behind the taskbar instead of being displayed in front of it. It happens way more frequently than with XP32. This isn't nearly important enough to affect my opinion of the OS, but it's a strange annoyance.
The only other problem I've run into is once or twice I forgot what OS I was running and tried to install the wrong driver, which of course led to nonfunctional hardware. User error, easily corrected when I realized my mistake.