Sorry, I cannot help you, but my iPhone 6 (not 6S) has the exact same problem. I get about half the benchmark score as I did with iOS 10.1. There is no difference when I enable low power mode. Everything seems to run and start slower. I believe the problem is caused by Apple's battery "fix" that came in iOS 10.2.1.
How it works is that it somehow detects that I have a questionable battery, either via serial number or measurements. Then it throttles down the processor speed to avoid power spikes that would otherwise have caused drops in battery voltage. It is these voltage drops that can cause unexpected shutdowns.
So for me, iOS 10.2.1 works better in that there are less shutdowns, but I have to accept that everything now runs at about half the speed, compared to iOS 10.1. This has been confirmed via benchmarks, which now run at about 40-60% of the speed from November last year. The lower the battery, the slower the phone becomes. It can also be seen from how enabling power save mode, no longer changes the benchmark scores. The phone always runs in power saving mode (the processor speed part of power save mode). I am not sure how I feel about this solution.
What can be seen from the public benchmark database for Geekbench, is that there now seems to be two categories of iPhone 6: 1) those that run as before, 2) those that run at about half the speed. I think that those that run at half the speed are being down-throttled to prevent unexpected shutdowns. If anyone can explain these benchmark differences otherwise, please do so. I would have liked my phone to run as it used to when it was new, I can always charge it before it gets to 35% or so, when shutdowns start(ed) to occur. And yes, I have tried a clean iOS install as New Phone, and run all benchmarks with Background App Refresh off and in Airplane mode.