I, too, experienced massive battery drain after updating to ios 6.1. After trying several suggestions listed here, I finally bit the bullet and went in to the Apple Store. The tech told me it was likely due to Microsoft Exchange, which I am tied into on my phone, to read email and calendar items from work.
Indeed, after, removing the old Exchange connection, and creating a new one, the problem seems to have gone away. If you are also seeing the battery drain problem, and you are connecting to Exchange, you may want to consider this could be the cause.
On the other hand, a friend of mine at work also connects to Exchange, and he saw no issues after the ios 6.1 update. So not everyone using Exchange is having problems after the update.. And if you have the problem and don't connect to Exchange, hopefully one of the other tips here will fix your problem.