I was having major battery issues on my iPad 2 and iPhone 4S right after installing iOS 6.
One thing I noticed is that when running Safari, the network indicator is always spinning even when it isn't running. I figured this has something to do with the reading list so I deleted all my reading list entries.
I then ran both the iPhone and iPad until the battery died and they powered off. I then charged them overnight to 100%.
That seemed to fix whatever was wrong as the battery life was great from that point on (*). Note, the same thing happened when iOS 5 was released. My thoughts is that the device needs to be recalibrated with each major iOS release.
(*) - This morning I notice battery drain issues on both my iPhone and iPad. Last Friday, my iPhone and iPad would both still show 100% when I got to work. This morning my iPhone showed 95% when I left the house after 1 minute of usage. My IPad was down to 99% when I got to work and dropped to 94% a few hours later, claiming I had 51 minutes of "usage", when I used it maybe for 10 minutes.
Things seem to have gotten better, but I have a feeling I'm going to need to restart both devices to get the battery draining at a normal rate. That's kind of annoying since under iOS 5.1.1 I never had to restart either device. Now it seems like I have to restart every few days because of some bug (battery drain) or another (WiFi issues). I hope Apple is working on a bug fix update.