This has been the most common question about iPhones for 7 years. It isn't something new. Also for every brand of Android phone except the Motorola, which has a humongous battery. Here's the text of a post I made earlier:
This happens to some iPhones after every upgrade or restore. Some app on the phone was active and was interrupted by the upgrade. When it came back up the app tried to resume and failed. You've got to find and kill that app. If you have an Exchange account that is the prime suspect. Go into Settings and turn off all of the switches (mail, contacts, calendar, notes, etc) for the Exchange account. Then reset the phone by holding HOME and SLEEP until an Apple logo appears. Once the phone comes back up turn the switches back on. Do the same for your iCloud account.
It can be other apps also. iOS 7 has provided a way to control background execution of apps. Go to Settings/General/Background App Refresh. This will list all of the apps that can run in background and use power. Start by turning them all off. If this fixes the problem turn on a few at a time until you find the perp.
Added: Have you enabled iTunes Radio? That's probably a huge battery hog.