In my experience this is an app issue more than an iOS issue. I guess we could call it an iOS issue, because if the battery monitor was at all useful(correct) it would save lots of work from the fix I am about to lay out for you...
As annoying as it is you need to go through and eliminate each app one at a time until you find the offender. I first discovered this after restoring my phone almost a dozen times one weekend to resolve this mess. I observed that when I had a blank restored as new phone with no apps my usage and idle times would return to normal(meaning the hardware and iOS are not the issue), but as soon as I restored my data it would go wonky again. Obviously this is caused by my restore putting back whatever is causing the problem... in my case it was the Shop Your Way Rewards app(itunes.apple.com/us/app/shop-your-way/id437521746?mt=8).
I found this by uninstalling apps one at a time, letting the phone idle for a few mins and then checking the battery time stats. This was a pain to go through and had the battery tracker built into iOS worked correctly we would not need to do this manually. Somehow through a fun coding error, behind the scenes tracker or some other nastiness that app was tanking my battery while not even getting reported to the usage menu. I assume it can not be the only app that causes this problem and if anyone finds out other offenders we should build a list.
TLDR: Restore your phone as new like you were about to sell it. Leave it in that new phone blank state for an hour(*DO NOT RESTORE YOUR DATA*) odds are it will resolve your issue with the battery stats being the same. From there just find the wonky app draining you and share it with the rest of us
Good luck and happy battery hog hunting
