I am 100% convinced it is a hardware issue, and it is the luck of the draw.
My wife and I both have a Lumia 1020 (RM-877), running 8.1. We both have HAD great battery life, even though she was on firmware 40000, and I was on 50009. I brought my phone in for repair, and they changed the phone housing to fix the problem. After receiving the phone back, I've had crap battery life, and I mean crap. I decided to do a test.
I erased my phone completely, installed no apps, turned off all background tasks that I could. My battery just tanked, maybe lasted 5 hours. Now I thought it was because she was on older firmware, so I downgraded my firmware to match my wife's. We were running the same OS version, same Firmware (40000), and I went through her phone and my phone, and I matched each option under settings and usage, and battery saver. Everything I could think of.
I at the time had about 65% battery, while she has 85%. We went out, and by the time 3 hours went by, I had 5% battery, and she had 65%.
She had Cortana enabled, and so did I. She had a tonne of apps, and I didn't. I didn't have Here Drive+, I didn't have Facebook, I didn't have twitter, nothing. She had facebook, instagram, 3 email accounts, BBM, Nokia Glace, High Sensitivity Screen, I only had my outlook account email logged in.
So there you go, my conclusion is it's a hardware issue, and it's the case housing. I think the battery may be electrically shorting with the case housing, and it's draining the battery.