My iPhone 5's battery also seems to be draining faster under 6.1. I haven't done any tests, but it sure seems like I'm having to recharge it more now.
I read somewhere that having LTE turned on will drain the battery faster, as the phone is constantly looking for an LTE signal (if not connected to wifi). Makes sense, as I was in a non-LTE area a few days ago, and my battery percentage charge went down really quickly.