There had always been speculations about the competing wireless technologies in the past, such as GSM versus CDMA. In this battle the scenario was different, where both the technolgies had a completely different interface for their operation, but CDMA proved to be far beyond GSM considering the number of subscribers in the market. It was also said that CDMA performs better than the GSM based interface. Every upcoming technology wants to surpass its competitor in some way or the other. At present, a similar scenario is observed with WiMAX and LTE. WiMAX deploying companies are in a rush to establish their very high-speed IP-based technology worldwide before LTE begins to mark its presence in the market.
WiMAX is being deployed at a steady pace worldwide and will try to grab major customers in the market. One must not forget the fact that in the U.S., North America's two leading wireless providers, namely, AT&T and Verizon Wireless has been roped to provide LTE services in U.S. And one must also not forget that Clearwire and other major vendors of WiMAX have already developed WiMAX base stations and is far beyond LTE deployment at present.
WiMAX would provide backhaul to the large customers and LTE may be roped in to provide access to them after 5 to 10 years down the lane. Originally WiMAX was being designed as a backhaul technology which may prove this technology to be a strong backhaul service provider. Neither of the technologies would displace eachother as the customers will have a choice of selecting the best option viable to them by considering the most reliable service provider, which is bound to be diversified within the masses.
Since Wi-Fi cannot be replaced totally by either WiMAX or LTE due to its vast recognition and usage by customers, it does not seem that LTE or WiMAX would compete thoroughly with each other, but rather be dependent on each other to provide valuable and high-speed services to their consumers with effect to their strengths and advantages.
Reference
Why the WiMAX Vs. LTE isn't a battle?