Here is what has solved this problem for me (it may not work for everyone):
I noticed that when this problem happens (battery drainage, hot phone, usage and standby numbers virtually identical), it happens on both my iPhone and my iPad, both of which run iOS 7.0.4, but not my iPod Touch, which has 6.1.5. I thought I'd gotten rid of the problem, and it came back -- on both devices running 7.0.4. It was suspicious that it came back on both devices at the same time.
I noticed that on both devices Safari seems to use a fair amount of data even when it's closed.
I noticed that on my Windows 8.1 PC, Apple IE DAV (which synchronizes IE bookmarks with iCloud) runs constantly, eating up 1.5% of CPU time, even when I haven't changed any bookmarks in days.
I concluded that the iCloud bookmark sync function is choking on something and causing iCloud to alert my iDevices constantly of updates, preventing them from sleeping. I disabled IE syncing in the iCloud utility. Immediately, both my iPhone and my iPad started to have differing usage and standby times: bingo.
I went out for the evening and found that my iPhone 5s was only using 2% of its charge an hour, even with mild usage, whereas before it had been eating up 15% just sitting on the desk doing nothing.
As it happens, I'm using Firefox much more than IE right now, so I'm going to rest and enjoy my iDevices, but I suspect that if I wanted to I could find specific bookmarks that are fouling up the system. It's silly, though, that it's even possible for any of this to happen. What if some hostile person really wanted my phone to get hot and die all the time?
Again, I suspect that there are multiple causes of our common problem, but if you use Windows, you might want to check your task manager to see if Apple IE DAV is hyperactive.