The rf transmissions of the handset are a pretty minimal part of the power used TBH, so I wouldn't expect the frequency to make any noticeable difference to the overall battery life used.
The power is really used in the signal processing which is independent of the frequency, and is the main reason that LTE takes more juice than 3G, and then 3G more than 2G, e.g the actual maximum handset radio transmission power allowed is actually 4 times higher on GSM than on 3G or 4G.