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!