To people posting small versions of panoramas: we can't see if the choppiness exists in such a small resolution. Zoomed out everything will look fine. It's when you zoom in where you actually witness the problem.
Gosubsgo. I've witnessed the exact same problem. On the 4s whenever I took panos of a room they all turned out absolutely fine no matter if the objects were close or not. With the iPhone 6 no matter what you do you will get choppy edges. (At least on my iPhone)
They changed something drastically on the software or there's a bunch of iPhones being affected by this problem. i have a hunch it's the software.
I tried the swiveling chair thing and it does work better but that was something I never had to do before!
When I get back from vacation I will do a photo comparison between the two phones and post the results here.