Same story as many here. iPhone 4s upgraded to iOS 6 yesterday evening then fully charged overnight.
First noticed something odd when I was tethering my iPad from the phone on the way to work and found that my iPhone battery charge had gone down a lot more than usual and it was feeling really warm. To fill in the detail I was tethering over bluetooth. I do this regulary and there is no doubting that this morning the phone temperature was much higher than normal.
I then stopped turned off personal hotspot (tethering) and carried on as usual with the phone with bluetooth left on as I normally do.
By the end of the working day I would expect to have over 60% charge but today it was at about 30%. On my way home it dropped steadily to 13% where it switched itself off and refused to turn on again.
I've recharged to 75% and restarted and cleared the list of background apps, not that that is likely to make a difference. I then turned off bluetooth and have managed to retain 75% charge for probably over an hour. I just turned bluetooth back on and the charge is now down to 72% within about 30 mins.
However, my wife's 4S has also dropped charge quicker than normal during the day with bluetooth switched off all the time but location services on due to some location aware reminders which have, however, been present for months. So, location services, if it is the problem for her, is a problem because it is causing more drain than normal.