Simply put, my understanding is that WiMax is basically 'super wifi', not at all the same technology as LTE, though both could be called '4G' in a very general sense.

LTE should be cheaper to build, mostly because towers can be spaced farther apart. It also has the potential to be several times faster than WiMax.

I live in Sprint's hometown, but I avoid Sprint like the plague. They know not what they do.