I've never had any issues as far as speed of opening things or responsiveness. What I have seen since 8.0 on my iPhone 6 Plus (and many other models, but particularly the Plus) is the low frame rate that animations run at. Especially compared to something like the iPhone 5 or 6 that have less pixels to push. This is noticeable in the control center, spotlight pull down, rotating the screen with spotlight open (stupid slow frame rate), quick reply, and sometimes the app switcher.
This is completely negated by turning on reduce transparency since it doesn't have to render as much but this makes iOS look quite ugly and it shouldn't have to be dumbed down to make it perform like it should.
It hasn't always been like this either, my iPhone 4s ran iOS 7.1 perfectly smooth and it had significantly less power. This is also noticeable on the iPhone 6s and 6s Plus as pointed out by Erica Griffin here (watch in 60fps). Shouldn't be an issue.
That being said, upgrading to iOS 9.2 hasn't changed my 6 Plus at all from what I can tell. Still drops frames where it has for the last year. It's no iPhone 4 on iOS 7, but still.
Quick reply is one area where to me its improved. But overall I feel like apple released the 6 Plus knowing it was under powered. Truth is the masses that buy these phones dont give a crap.