All,
If you have phones that are older than 1 generation back (ie: older than the iPhone 5), you are going to see battery drain increasingly with each new version that comes out. That's how operating system updates work. Works the same way with the Samsung S4, etc.
I've had the iPhone since the iPhone 3 came out and I upgrade every 2 years. I've always noticed that right around my 2-year mark that the operating system has required much more hardware capacity and that my phone's hardware at 2 years old has become outdated. THUS, with my processor working doubletime in my phone, the battery will drain much faster.
If you are operating with anything older than the iPhone 5, you are going to experience significantly more battery drain with each operating system update. It's just the nature of operating systems requiring more hardware capacity because they assume that most are updating their phones regularly to handle it. Outdated phones will experience outdated problems like battery drain.
By the way, my 5s is fine now after updating apps that I most often use and giving the phone a "Hard Shut Down".