Even though WiMax is rolling out in some portions of the country, LTE will be the next standard. By creating an all IP-based network it will unify mobile and fixed broadband worlds. Here's a great resource
for information on 3G and 4G news.
The WiMax camp positions it the two as complementary and not competitive. In this post
the author suggests that both will find a place in the market and that WiMax simply suffers from too much hype, too early in the process and is now paying the price while LTE appears to be a newcomer with all the "shininess" that comes with that role. WiMax was designed for backhaul applications and will continue in that role and LTE will find its applications as well.
While Wimax is seeing substantial growth now, the major carriers will role out LTE capabilities in the next 3 years. According to this post,
the other major competitor will be HSPA.