LTE Won the Race for the Next Generation
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.