He is right
There is little network difference between the two. Both rely on IPv6/Mobile IP. LTE PDN gateway can very happily be a WiMax ASN and vice versa. Similarly, the backhaul can be reused and shared and so on. Similarly, you can control services on a WiMax network using IMS (if you are crazy enough to do so) instead of using WiMax MAC layer capabilities.
The "who is winning" is pretty much a storm in a teacup brewed by journos and pundits. Both architectures are interchangeable and can be mixed and shared provided that you stick to the more generic principles and not go into a feature frenzy.