The folks at my Apple store reloaded IOS 6 for me a couple weeks back,and I don't know if they did it by DFU or some other means since they did it where I couldn't watch them,however...since they fixed my 4s for me I have had much battery life than I did with 5.1.1. firmware.
I did have to reload all of my apps 1 x 1 and I lost all of the pictures I had taken and all of the movies I had loaded,but all of my contacts were there.
Whatever they did has made my phone work as it is supposed to work,including the maps,wi-fi,and Siri. Prior to them fixing it,none of those 3 would work properly and I had a real issue with battery drain for a couple of days. They told me there I had a incomplete download of the new OS and was the cause of my issues, which could be the reason so many folks are having problems with theirs.
I can't say it will correct any issues with yours,but it made mine work great.
FWIW...when I was a Android fanatic...this was a known issue of happening with any OTA updates, and would cause similar issues too.
So, for myself,I see no reason to go back to 5.1.1 unless your wanting to Jailbreak your phone because on my phone my battery life is actually better.
Mac