The fact is both the 6s and 7 are very fast. The fact also is that the 7 has a newer and faster process in terms of benchmarking and potential. Is that extra horsepower being utilized for every day use? Most likely not since the 6s already performs daily tasks very well.
So what about these youtube videos floating around? For starters we have no idea if the phones being used to compare are being run in indentical settings without stuff going on in the background that might affect speed. In addition, I've read some comments regarding the A10 operating a little differently to help conserve battery life. So just because some random app opens half a second faster on the 6s doesn't mean it's faster. It's a silly arguement.
In any case, all of this should be a testament to how well Apple has optimized iOS 10, as not too long ago we were seeing lag in iOS updates even in phones only 1-2 years old. I've heard nothing but positive comments about iOS 10 on even 5s devices, so that is a testament to how well the operating system has progressed in terms of legacy support.
In terms of the A10, we are reaching the point of maturity with smartphones that you aren't going to notice huge differences in everyday speed as the older devices, especially the A9 already handle that well. Unless you are playing games that push the hardware, you likely won't notice it. That doesn't mean that Apple messed up or lied, but rather that this technology has evolved to a point that even older devices are so fast and powerful that everyday use will not be affected.