Specifically, is the 64 bit version of the ISO I can download directly from ubuntu.com the same as the "alternate" 64 bit version that is available through the Universal USB installer?
The two versions are simply different installers, and will both install the same version of ubuntu. The alternate installer is meant to be used if, for some reason, the regular one doesn't work. The end result won't be different though. I would recommend that you use the regular installer whenever possible as it will offer a more user-friendly experience, but you can always use the alternate version if need be.