I can't prove it but based on my experience with my previous Mini 2 (A7) Apple seems to build new versions of iOS with the newest chip in mind an if it works well with older chips, fine, but it's not any kind of priority. So with iOS 10 my mini2 started to slow down like an overheated dog. Scrolling, Safari, just basic things, nothing really taxing. I loaded up the iOS 11 beta on it and after a few updates of that OS realized it was time to dump the mini 2.
I have the iOS 11 beta on my Mini 4 and fast enough but I suspect iOS 12 will likely bring some slow downs. So yes, the chip does matter even if you are just using the iPad to skim the Internet.
As to which of those two iPads you should get -- depends on how long you intend to keep it. The Air 2 has an A8X. The iPad Pro 9.7 an A9X, which is actually faster than this years non-"Pro" iPad. If you don't really need cellular new iPad Pro 9.7s have been regular on sale for just a bit more than the 2017 non- "Pro" iPad. As holiday sales start to crank up should be seeing more of those sales.