No such problems on my 4S. I got 7 hours of screen time on iOS 6 and I get 7 hours of screen time on iOS 7. Parallax effect off, bluetooth off, auto update apps off and all other stuff off that was off before.
Now it seems the battery life improved so much that it's actually now better than iOS6....
Now it lasts more than 24 hours with moderate usage. My Skype is always opened as well.