Battery issue - backup problem? I recently bought a new iPhone 6, because my iPhone 5 had some weird battery issues: when I was on 3G or 4G, the battery would literally go down from 50% to 10% in like 10 minutes. On the Wi-Fi, it was pretty OK. 

Right now, with my new Phone, I was expecting way better battery results. But weirdly enough, it's still pretty bad, though the phone is new. 

I went to the Apple Store a couple of weeks back with my iPhone 5 and the guy told me that it may be a software issue (related to my backup, which I put on my iPhone 6) and not a hardware issue (don't worry I didn't buy the new iPhone just because of that).

Anyways, I was wondering if that could be a logical explanation?
And then, I would like to try completely factory restoring my phone to check but there are some settings like the wifi passwords, etc. that I'd like to keep...how can I transfer them without the backup?

Thanks a lot!
You should first make a full backup and restore the new iPhone to factory default. Don't worry about your settings, it's stored in the backup so you can place it back if you miss something. Or you could try this fix on the iPhone 5 first.

Problem resolved?
If the problem is gone you shouldn't place the back-up back, as something might be damaged inside. You can now manually download every app and add the Wi-Fi settings.

Unfortunately: You cannot put any part of your back-up back, as it's damaged somehow.

Please
Please don't worry about Wi-Fi settings. You can always ask everyone for their passwords (at least in my circles) they're given out pretty easily. You rather have a fully functional phone and battery rather than all Wi-fi passwords, don't you?

Please note I didn't add an answer to when restoring to clean default does not fix your issue.