This is an old post based on excerpts I read from the web. Adding it back.
This post will cover the technological differences between these two technologies and contains a brief bullet point description as to why LTE took off and WiMAX did not:
Slot times: LTE uses much smaller slot times - 1ms as opposed to 4ms which gives much worse delay performance with multiple users and does not scale just as well.
Uplink modulation: LTE introduced SC-FDMA which dramatically improved uplink performance for cellular systems. This modulation technique combines the advantages of low peak to average ratio of traditional systems (such as GSM) and multipath resistance of newer modulation schemes (such as OFDM). SC-FDMA also provides savings for the mobile users (on their uplink).
Timing: WiMAX was the first to start off. Hence most of the experiments were performed on this and LTE could learn from their experience and MISTAKES. WiMAX was initially designed for fixed systems rather than mobile systems and they were not able to adapt well for usage with cellular providers.
Other non MAC/PHY differences:
WiMAX is based on IEEE standards (specifically, the 802.16 family), and then managed by the WiMAX Forum. LTE is defined by 3GPP.
WiMAX was originally designed for fixed networks and has gradually evolved into a mobile network. But this has resulted in some changes not being made correctly. LTE was designed as a mobile network from the first day. This particularly impacts the power at the receiver (handhelds). WiMAX handhelds are slated to consume more power as compared to LTE.
