My 6s plus also stutters on Twitter, more than my 6 plus does, it's very annoying. I expected it to be better than the 6 plus in smoothness terms. The music & podcast apps both stutter slightly also. The weather app is buttery smooth now though.
not sure what it is but I just updated my iPad to iOS 9 and twitter suddenly became laggy like my 6S. My iPad ran it without any choppiness in 8.4. I wouldnt say its terrible lag but its not as smooth as it used to be.