Don't take this the wrong way, just pointing out the facts.
First of all this thread is about the iPhone 5 not the 4S.
Second that video is not s fair comparison. Different apps and something wrong with the 8.1 install. If he reset erased and restored than it might be closer to fair.
And yes i'm shouting! We've had nothing but problems with battery decreasing fast and we've even changed the battery. I wish i could downgrade back to 7.1.2.