Resurrecting an old thread, but I guess still relevant...
As for LTE reducing battery time... Not sure how accurate this is, but supposedly some studies have shown that you can get better battery life with faster connections, even though they use more power.
Well, with a faster connection, downloading the same web page is faster, allowing the radio to go into low-power state sooner. For example, if the radio takes twice as much power, but if the page loads 5 times faster, then overall you will be using less power.
I'm not sure how true that is but that is what I heard.