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LTE Home LTE Intro Data rates CAR of 4G SL Mobility EPC Arch Interfaces LTE Cells Multi Antenna Access Tech LTE Frame Alt Frame PHY Layer LTE vs. CDMA LTE or WiMax LTE VOIP
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LTE (Long Term Evolution)

Detailed LTE introduction can be referred from this link.

In brief LTE is a fourth generation (4G) wireless standard for broadband mobile technology. This standard is developed to meet long term future requirements of higher data rates, lower latency, better cell coverage and seamless handover.
Comparison of LTE and WiMax or LTE vs. WiMax

1. 4G LTE or WiMax Technology -

3GPP (3rd Generation Partnership Project) has created a 4G all IP core based LTE technology.  Details at this link.

IEEE 802.16 and WiMax forum has promoted 4G all-IP based WiMax technology.

2. 4G Coding Technology -

LTE uses OFDMA for downlink and SC-FDMA for uplink transmissions.

WiMax uses OFDMA for both uplink and downlink transmissions.
4G LTE and WiMax comparison.
Introduction of 4G LTE and WiMax followed by LTE  vs. WiMax comparison.   
WiMax (Worldwide Interoperability of Microwave Access)

WiMax is a name of organization which is responsible for promotion of Boradband Wireless Access (BWA) technology defined under standard 802.16. The end-to-end network architecture which supports WiMax networks is controlled under guidelines of  WiMax forum. This architecture is also based on all-IP.
Evolved Packet Core (EPC) system architecture for all IP.Mobility Management Entity (MME),
Serving System (S) Architecture (A) Evolution (E) Gateway or Serving Gateway SGW.
Packet Data Network (PDN) SAE Gateway
Enhanced Packet Data Gateway (ePDG)
Multiple antenna techniques - MIMO, Adaptive antenna systems - AAS and Antenna diversity - AD
Cloud Computing ?
Whenever a document or photo is uploaded on the web, a thread of cloud computing is active. Learn more from here.
3. LTE and WiMax Duplex schemes -

LTE and WiMax supports both FDD (Frequency Division Duplex) and TDD (Time Division Duplex).

4. Radio Channel -

LTE and WiMax both supports flexible carrier bandwidths from  1.25 MHz up to 20 MHz.

5. 4G WiMax or LTE Data rates -

LTE FDD supports very high data rates, best in industry. Peak data rate for 20 Mhz spectrum is around 100 Mbps in DL and 50 Mbps in UL.  Refer this section for details.

WiMax FDD also delivers very high data rates upto 128 Mbps in 20 MHz for downlink and 56 Mbps in 20 MHz bandwidth for uplink.