I'm having all the same issues in my 6 plus. I have restored as new, reset settings, tried 9.1 betas and still laggy as ever. I wonder if it is affecting certain models. Mine is a 128gb.
I thought it was a model issue too because I have the 64gb. I just wish there was a fix and it may be that it's not enough RAM but man it runs smooth on my 5S I have for work...
Mine seems to do better if I reduce the transparency.
Not sure what the transparency would have to do with it...
After doing a lot of searching and sifting through forums, this was recommended many times. I tried it and it cleared up the laggy transitions. Must have something to do with the way the 6 plus scales.
I'm going to try it. What did you put your transparency on
Go to Settings/General/Accessibility/Reduce Transparency.