To be specific, the Exchange-related issue that seems to be present in iOS 6.1 is around the calendar and events handling (vs. mail or something like that).Do you have an Exchange email account set up on your phone? This has been suspected of being the cause of the battery drain issue due to excessive network communication. My iPhone 5 has had worse battery life on 6.1 and I'm using Exchange.
To be specific, the Exchange-related issue that seems to be present in iOS 6.1 is around the calendar and events handling (vs. mail or something like that).
What I noticed is that my phone now has trouble jumping from 4G to LTE in LTE coverage areas. This was not an issue for me prior to 6.1. I'm also seeing a decrease in signal strength and "Searching" in my office where I've always had great service (i5 ATT in Manhattan). My battery left at end of day with 6.1 is less with similar usage patterns, likely because of this.
I updated through iTunes and then restored from an iCloud backup (which was a backup created new under 6.0).
I'm hoping for a 6.1.1 updated for the i5 as my issues seem similar to what was addressed in the 4s update.
My iPhone 5 battery life on 6.1 is terrible!
I have removed my gmail and yahoo email that were setup in the exchange and now using the Individual apps instead. Result is no more battery drain and no heating
.... But I am no longer able to email my attachments straight from other apps using the share option.
I've just resorted to charging my iPhone and iPad more often until a bug fix is released.
May I suggest that before you change accounts or the way they are set up or the way you use the phone that you do a restore of the phone (or have an Apple genius do it for you). I had severe battery drain and heating up issues immediately after updating to 6.1. The restore fixed it and no further problems. Apparently a certain number of users have gotten bit with this issue with each update. 6.1 was my turn I guess. But the restore fixed it all.