That is absolutely... incorrect. You are apparently basing your post upon the commonplace, but bogus, idea that LTE is natively GSM compatible.
It is not. LTE has been chosen by GSM carriers, but that does not make it GSM. LTE has also been chosen by CDMA carriers, but that does not make it CDMA either.
In other words, CDMA -> LTE is the same as GSM -> LTE... each has to move to a totally different air and backend interface.
Actually, moving to LTE is slightly easier for CDMA carriers, as they are far more likely to have already implemented massive IP backend networks, which LTE is based upon.
Verizon has it all over ATT for 4G, as Verizon has invested heavily not only in the airwave auctions, but in fiber backhaul. Moreover, Verizon is defining the equipment, since they're first implementers.