iPad 3 16G WiFi 3G (upgraded on evening of the 18th)
I only use 3G when traveling, mostly for GPS, so I can't comment on what impact it might have. I'm usually within range of a WiFi signal otherwise.
I'm also having battery drain problems with my iPad 3. I purchased it new when they came out and have used it through all the IOS 6 upgrades without any problems at all. Under IOS 6 I was able to run all day (most of the time) and still have 30% or more charge left at night when I put it on the charger. I've tried all the IOS 7 battery saving suggestions I've found on the internet with only a small battery improvement (roughly 10% or less after doing a RESET).
I used to be able to do a full charge overnight but the highest charge level I've seen since I upgraded to IOS 7 is 91% (wasn't fully discharged when I put it on the charger). If it has shut down due a low battery it usually runs around 65% after an overnight charge (roughly 11 PM to 7 AM). Just to be sure this wasn't caused by a hung app I've started hard booting it each night (assuming the a low battery hadn't already shut it down) before I put it on the charger without any further improvement.
One thing I've noticed that I haven't seen mentioned is my iPad runs warm even when it is just sitting arround with nothing running. It has always run warm after a full charging session or extended usage session but I have never noticed it being warm when I pick it up after having it just sitting for several hours.
I'm not using the smart cover but I have my iPad set to turn off after 5 minutes of inactivity. I'm using the original Apple charger and cable that came with my iPad. I have a second charger and cable purchased from Apple that I use when traveling but it does the same thing. Hopefully Apple will resolve this issue quickly. As many people have mentioned doing full charge/discharge cycles is really hard on the battery and shortens it's life greatly.
I also have 2 x 4S iPhones (AT&T) which I upgraded to IOS 7 without any problems (mine on the 18th and my wife's on the 21st after I had verified my upgrade was working correctly. We all upgrade our personal equipment and verify them before upgrading our wife's, RIGHT!!! :>)