Hi;
I think that WiMax has a long way to go. For LTE, we have the raw material, engineers are used to think LTE (UMTS...) and moving to LTE is closer to happen than redeplying another technology.
However, some people are pessimistic and predict a mixture of LTE with WiMax in the 4G coming networks. "It is not about speed, but capacity" said some of them. This means that, the capacity of LTE networks could be limited because of the growth of the traffic and the iPhone effect.