What's your claim of LTE offering better battery life VS 3G based on? The battery test that Anandtech designed for the iPhone5? I personally can't put much faith in this particular Anandtech battery test:

It doesn't jive with my personal experience using the iPhone5 on LTE and 3G

It contradicts Apple's own battery life claims

Devices with the old SOC get dramatically different results on the new test (see for example the results for the HTC OneX in Anand's initial review and compare with the results in the iPhone5 review chart).

The claim isn't that LTE has better battery life vs 3G. Instead it is:

LTE battery life with today's SoCs vs 3G on today's SoCs > LTE battery life with last year's SoCs vs 3G on last year's SoCs

with the suggestion is that the improvement is significant enough that LTE battery life isn't the problem it used to be. None of that claims that LTE battery life today is better than 3G battery life today.

IIRC this is still a problem if your carrier doesn't fully support LTE, i.e. you still need your 3G radio switched on to receive calls.

This is one reason I'm excited about the Google-Dish wireless carrier news. If they made a 4G-only carrier, you could use VoLTE for calls. By removing the need for non-4G chips, phones would become lighter, smaller, cheaper, and less hot when running. And hopefully service would be cheaper and more stable too.

Doesn't seem to make a noticeable impact on most recent VZ phones, and as far as I'm aware VZ doesn't run VoLTE[0] yet.

[0] Anecdotally, I'm hoping that's right. I've been on (GSM/UMTS) T-Mobile for years and switched to VZ a few months ago; and I've noticed a marked drop in call quality & stability vs. every GSM phone I've owned.