As it turns out, not all new iPhones are created equal. There's two different versions of the A9 processor, and while they're mostly the same, one of the chips seems to be killing battery life.
As Anantech noted shortly after the phone's launch, there are two different A9 chips: one made by Samsung on a 14nm process, and one (slightly bigger) by TSMC. Apple sourced the chips from two manufacturers in an attempt to reduce the supply problems that are normally a hallmark of iPhone launches.
But the two chips don't work exactly the same. Although they benchmark with about the same power, the battery life (and excess heat) is different. According to posts on forums and some Chinese sites, phones with the TSMC processor get two hours more battery life on the Geekbench battery test, while running a few degrees cooler.
Obviously, that's not definitive -- not least because battery test apps tax processors in a particular way, which doesn't accurately reflect real life. If you want to find out which processor is in your shiny new phone, the easiest way is to download the free Lirum Device Info Lite app, and look at the model number on the main page. N66AP (6s Plus) or N71AP (6s) means a Samsung chip (and supposedly lower battery life), while N66MAP or N71MAP means the TSMC chip, and some peace of mind.