The air 2 is much smoother in all the areas you mentioned accept when rotating in spotlight. It's a little jerky. I chalk it all up to bad coding since the iPhone 6 plus has many stuttering issues reported all over these forums.
There are still a few minor annoyances even on the air 2 like scrolling through music, slight jerkiness. Happens on my 5s too. That seems like bad coding to me. Also weird photos app lag when tapping an image in camera roll only. Weird.
Let's hope it's bad coding, because that means it can be fixed. It's just a matter of whether they decide to or not.
The Mini 2/Air 1 are stuck in a really sad state of UI stutteriness between the iPhone 4s and iPhone 5. We are seeing performance equivalent to 2-3 year old devices, when these iPads have barely been around for a year!
I can't wait till the next time I can visit an Apple Store or a Best Buy and actually am able to use an Air 2, then I can finally assess how gimped the Mini 2/Air 1 are. If the Air 2 is indeed perfectly smooth in most of the areas I mentioned, then the mini 2/Air 1 are definitely underpowered. If the Air 2 lags as well, it's bad coding, and I can be hopeful for performance updates.