iPhone 5s with extremely poor battery life on 6.1.3

For the last couple weeks or so the battery life on both my wife's iPhone 5 and mine have been terrible on Verizon. I'm not sure if a carrier update was pushed or of apple is making behind the scenes changes to the software and the server connection side. Putting some posts out to 3rd party websites and looking online seems to verify the matter.

Doing what I vowed not to do, I called Apple care and got some rude rep who said there are no known issues with 6.1.3. Just because it's what they are instructed to say doesn't mean it's true. I asked how come we didn't have these issues prior to upgrading the phones, and was told the software was fine. I've tried recline acting the battery, restoring and setting up as new, and keeping most features turned off. It seems as though the antenna for wifi or LTE is the culprit as it drains rapidly when connected and runs hotter than it did before the update.

Anyone had any success in a fix or setting tweak. I can't rely on apple tech support to fix this as they just give the automated responses without care or concern. Already eyeing the HTC one or S4 as I need stability, not leftover software patched together.