New device, New iOS, battery issues here's what you do...
OK so over the years I have heard my fair share of battery complaints on forums and from friends in general. I have heard the usual stuff ending with setup as a new device. Now to me that should be the last resort. The backups are there for a reason and some people can't lose their messages, settings, etc. I have hardly ever had battery issues in the 5 years that I have owned iPhones but once in awhile it seems like when new iOS versions are released my iPhone goes crazy and the battery starts to drain like crazy. So here is what I have observed from my latest bout. Try this before setting up as new and it just might help allowing you to keep all of your data and settings.
Update all your apps, then sync in iTunes and Transfer all purchases(right click the device and choose the option)
Unsync all media(not apps) off the device, music, photos, podcasts, movies, etc. basically go to each tab and uncheck the sync option.
(you will want to make sure you put all the photos on your computer, also if you have a long list of apps you might want to take screenshots so you know which ones to put back on)
Delete any apps that aren't stock apps, except apps that will require login information after re-install
Turn off mail accounts
If you're jailbroken take off any themes, you can leave tweaks but apply any updates and while cleaning up get rid of tweaks you no longer use
Restart the phone
Plug in the power then power the phone off and let it charge for 2-4 hours whatever it takes to be at full charge
Once fully charged use it for a couple of hours then sync all your media back onto it
Install all the apps again but do it from iTunes because it will have the most up to date version
Turn your mail accounts back on and reboot the phone
Use it like this for another couple of hours
Apple your themes and after the respring reboot the phone again
This is sort of like a spring clean and has worked for me on both my iPad and iPhone. So give it a try and hey it might save you from losing all your settings, I do it on new devices and also after I do an upgrade to the OS or if my battery has been working fine and then just starts draining like crazy.