Don't you think you need to check the battery?
Especially for iPhone 5S

I compared two iPhone 5S, both freshly installed with iOS 8.1.2
One of them is the 6 months old, and the another is just 2 months old
My method.
1)Make sure both of them run out of battery, then start charging both of them with similar original cable and adapter with same power source.
2)After it turn on automically, I shut down both of them(Technically, they are still charging)
3)Charged both of them until fully charged to 100% (around 4-5 hours, trickle charging)
4)Both of them in airplane mode, in the same settings(brightness/lock/etc..)
5)Wait until both of them dead.

Apparently, the 2 months old iPhone 5S performed better, and last much longer.

So, for me, the iOS 8.1.2 is good, the difference of battery performance is not because OS, but because of battery.

After replace the battery, you can see the significance difference