I have a 6+, 64GB which has been performing poorly on iOS 10 as reported by many in this thread. Some of the stock iOS apps were very slow: it took a very minimum of 4 seconds to launch Messages or the camera for example. My phone has 12GB of free storage.
I spent quite a few hours, preparing the phone to be factory reset. My initial plan was to manually restore my apps/data afterwards, through a mixture of off-line backups (photos) and iCloud sync features. Then I realized that there are some stock iOS apps (activity and health are the two I discovered) whose data can't be restored other than through an iTunes or iCloud backup. So the "solution" advocated by some of performing a factory reset without restoring a backup really cannot be qualified of such unless you're happy to loose some potentially very valuable data...
(Very) long story short, it took a good 4 hours to get my phone back to its former state, which entailed re-syncing my iTunes library. Needless to say this last point didn't complete cleanly and I'm still left with dozens of "ghost" songs, but that's another massive long standing Apple fail story which is told elsewhere.
Then my Apple Watch also had to be reset and took another hour or so to restore.
Next, I had to interact with call centres of two banks and one store card, whose apps had de-activated themselves due to the reset. In one case, I had to wait for a snail mail letter for functionality to be restored.
All in all, this little dance wasted well over a day of my life but I thought it was worth it because my iPhone was indeed back to something usable (meaning opening Messages now only took only about 2 seconds). However that joy was short lived because a couple of weeks later, the phone is back to its sluggish, barely usable self.
My gut feel is that the issue is down to the lack of RAM in the 6+ (only 1GB). This is certainly not to be read as an apology of Apple, even if they only "accidentally" figured out that doubling the RAM in following gens and piling up on memory requirements in iOS 10 meant that it accelerated the obsolescence of that particular (6) generation.