I don't know what I did that is different, but I am getting better battery life with iOS 6.1 on my iPhone 4S (32 GB model) than I did with 6.0.1 which wasn't that bad.
I did the update through iTunes because most of the reports I have read from people who are having problems did their update OTA.
I did a full sync to make sure all apps were downloaded to iTunes. I followed this up with a full manual back up to iTunes.
I then shut down all apps in the multitasking tray and restarted my phone, Home button and Power button held down simultaneously until the Apple logo appeared and the phone restarted. I double checked the multitasking drawer and shut down the apps that reappeared here and restarted my phone again. This time the apps were gone from the drawer.
I plugged my phone into my computer and connected it to iTunes and ran the update. It took about 20 minutes to finish but I had no problems during the process. I also always leave my PC alone to do nothing but update my phone, I just go get coffee and watch TV while waiting.
Once it was done I went through the start up process and once that was done my phone was updated and all my apps, photos, media, etc. was still there, none of my home screens had been rearranged. It was just my phone with iOS 6.1 running.
I watch the battery percentage and it stayed at 100% for about an hour. I really didn't do anything with my phone during that hour other than tap the Home button to see what the percentage was just to see if anything was going on with the battery life.
After an hour of this the percentage dropped to 99%. I then started using my phone normally and the battery was fine. In fact it seems to work better than ever. I surf a lot, check mail about every hour or so, play games, look up lots of stuf on IMDB, and listen to lots of music.
So far I am very pleased with my phone on iOS 6.1. I may try turing on some of the things I had off in the past to see what happens.
I was comfortable enough with iOS 6.1 on my phone that I also updated my iPad 2, 32 GB WiFi + 3G and it also is running fine and gets great battery life. I followed the same routine with my iPad update that I did with my phone.