Will 802.11n Replace WiMAX?

Working Frequencies
WiFi 802.11n works in the unlicensed 2.4Ghz ISM band and 5GHz U-NIII bands. WiMAX 802.16e utilizes licensed frequencies between 2Ghz and 11Ghz and the choice depends on the license a particular operator has. This is also dependent on what band a country has allocated for licensed WiMAX operation.
Coverage Range
The coverage range of WiFi 802.11n is about 400 meters in open spaces but will be lesser indoors. For WiMAX 802.16e, coverage distance can be metro-wide and can be more than 50 km.
Speed
WiFi 802.11n was developed to provide faster speed (around 300 Mbps) than the a, b and g variants of this standard. WiMAX on the other hand can handle speeds up to 70 Mbps. It should be noted however, that for both standards, available bandwidth is dependent on many factors such as the distance from the base stations or access points, RF environment and the number of users connected.
Quality of Service
802.11n and WiMAX have different Quality of Service (QoS) mechanisms. This feature is standard in WiMAX and utilizes a method based on type of connection between the base station and the user device. WiFi has introduced a QoS mechanism where certain traffic flows can be prioritized over others. For example, VoIP or video streaming applications may be given priority over ordinary web surfing.

Target Market
WiFi, including 802.11n, was primarily developed for wireless local area networks (WLAN) with a limited coverage area. It has found popular usage in last-mile delivery or consumer applications, such as hotspots in public places, offices or at home. WiMAX, on the other hand, was developed primarily for wireless metropolitan area networks (WMAN) with coverage ranges of up to several kilometers. Service is usually subscription-based and provided by telco operators intended for business users. Example applications are as backhaul for wide area networks or internet connection for ISPs.
While WiMAX have been around for a number of years and slowly making inroads in the wireless broadband industry, the proliferation of 802.11n-equipped devices is happening at a faster rate.  More and more devices such as laptops and routers are now being equipped with 802.11n, making it now possible to run bandwidth-hungry applications like VoIP and video streaming.
Maybe 802.11n will not kill WiMAX after all. It can be safely said that both standards will further mature for they have different applications and may actually complement each other for the years to come.