Two different frequencies. Wimax and LTE technically aren't compatible. Wimax runs on a higher frequency, which is why it has problems with building penetration. LTE runs on a lower frequency which should (theoretically) give them better building penetration.
They're not compatible, but the frequency doesn't matter.
Currently, WiMAX equipment makers are only producing radios in the 2.1Ghz spectrum, but they could build 700Mhz units if their customers asked. Ditto for LTE. For example, right now there are 800, 900 and 1900 MHz versions of CDMA and the same chipset makers could produce 700, 800, 900, 1900 or 2100 MHz LTE or WiMAX chipsets if their customers asked. They build GSM chipsets all over the PCS spectrum. It's all a question of where they own spectrum.
You are correct that the frequency definitely DOES impact building penetration. But the low-frequency designs need wider spectrum to get the same bandwidth, so your better indoor coverage won't be as fast. It's all a compromise.
If you read the specs, WiMAX and LTE are really, really close. Less than 5% different, really. They are both code division instead of time division, both use OFDM, both use the IP stack, both have the same call control, etc. It's almost all a difference in software, not hardware. Specifically, they differ in the uplink protocols but are practically identical on the downlink. It's that uplink chipset that's the sticking point.
In fact, the chipset manufacturers are pushing them to merge in a future release of the specs. WiMAX's only advantage was its immediate availability. Right now, they're talking publicly about building "god chips" that can work on either. If any carrier switches from one to the other, they'll put these "god chips" in their base stations and build an overlay network so your legacy device won't become obsolete. That's why Sprint and Clear are so nonchalant about LTE. They'll buy whatever the vendors are peddling cheap.
So go ahead and buy that WiMAX device right now, you'll be fine. If you're on a two-year contract you'll be ready to upgrade by the time the two specs merge anyway.
--Q-fugee