iOS 6 bug - battery draining, details below
I was also getting terrible battery life after upgrading my 4S with iOS 6.
Turns out there is a bug involving iCloud syncing of Safari.
Take a look in Settings > About > Diagnostics, and look to see if there are a whole bunch of crash reports for the process "webbookmarksd". I had a hundred or more.
This is the process that syncs Safari bookmarks to/from iCloud.
I have found that, after restarting the phone, as long as I don't run Safari, battery life is great - possibly better than the same phone on iOS 5.1.1.
However, as soon as I run Safari, the webbookmarksd process starts to chew up CPU, the phone gets hot, and the battery starts to drain very fast - 10-25% per hour.
Seems as if some kinds of bad bookmark data can keep crashing this process, over and over, so that it keeps trying to complete the sync and never can.
(Come to think of it, I had a similar problem upgrading my old 3GS from IOS 4 to 5.1.1 - except it was a calendar sync bug in that case.)
Turning off iCloud syncing of Safari doesn't help. Neither does force-killing Safari from the multitasking bar. Putting the phone in Airplane Mode helps temporarily, but when you turn Airplane Mode off, it just starts right back up again.
Deleting my Safari bookmarks on my Mac and allowing those changes to sync also hasn't helped. And there appears to be no way to force iCloud's to reset its version of the bookmark database and push empty bookmark sets to the phone and Mac. Unfortunately, because otherwise I could clear everything out, then restore from a backup on the Mac and let a good set of bookmarks sync back over.
I'd be curious to see if anyone else has run into this - there were a few people on the discussions.apple.com forums that had similar issues.