I don't know what the problem is. I just know that my first 5S constantly rebooted but my 2nd and 3rd didn't reboot a single time.
Maybe there was some corruption somewhere. Thats possible. But its up to Apple to make sure things clean up and install properly on all other devices so that people dont have these issues. So far its been a crap shoot.
My iPad 4 likes to re-spring every now and then especially when entering multitasking or sometimes using iTunes radio. Many of my other apps I use constantly have worked perfectly fine in iOS 7 including many games. Its definitely and iOS 7 issue one way or another. All my crash logs indicate its a "springboard" crash. Thats core system interface issues.