If the device is restored from a backup, it is not being restored as new. The process is one or the other but not both.
If the device has been used as designed, contacts and calendars are synced with a supported application on the computer or a cloud service.
Pictures and videos taken with the device are designed to be regularly copied off the device to a computer for safe keeping.
Content acquired from iTunes (music, videos, apps, etc) should exist in iTunes on the computer for safe keeping. Regularly transferring purchases to iTunes ensures the content is safe as not all content can be downloaded again.
Before restoring as new, try a reset and restart. The bad battery life could simply be the result of a rogue app running in the background.
Also, go through the apps in Settings > Privacy > Location Services and ensure that there are no rogue apps there that do not need (or you do not want to have) location access. I've run across a few horribly written apps that leave location services turned on all the time and will kill a battery in no time at all.