In my case I'm having better battery with HSPA than with LTE.

The thing in my house I have yellow/brown 4G signal and green 3G signal.

In a long deep sleep time (at nights) 4G consumes a bit more than 3G.
But during the day the difference is a little more significant.

I can get 4 hours of SoT with 3G. But 3 hours with LTE (or 3 hours and half).

I'm pretty sure that with a perfect LTE signal I would even have better battery life (like almost 5 hours of SoT).
But here is still experimental.
Nexus 5 (Stock + Franco Kernel) - Galaxy Nexus (CM11 + A.S.K.P. Kernel) - Nexus 7 2012 (Stock); Galaxy S GT-i9000 (CM11 - zRAM OFF); Galaxy Y Pro B5510L (Stock).
Nexus 4 16GB; Galaxy S3 GT-i9300.