Will iOS 9 reject an iOS 10 backup restoration attempt to the same model phone? From what I've been reading, people say you can't restore a phone that is running iOS 9, from a backup of the same type of phone running iOS 10.  I'd like to know what happens if you try.  Does the phone simply not recognize the restore attempt?  If using iTunes, will you be told the device is incompatible with the chosen update?  What about OTA, what happens there?

To be clear, I'm not at all referring to restoring/downgrading the OS.  I have an iPhone SE that was unintentionally updated to iOS 10, so now I got an identical iPhone SE running iOS 9, and I'm curious to know what happens if I tell this second iOS 9 phone to restore from a backup made of the first phone after it was updated to iOS 10.
You won't be able to select an iCloud backup that contains data, settings and apps from a newer build. In the past, there wasn't helpful information explaining you need to update the iOS - now generally you get an explanation.

On iTunes with a USB backup (or Apple Configurator), you get similar experience - you don't get to attempt the restore as code to check prevents the operation from starting.

What you can do is sync data using iCloud and possibly computer / cable / third party apps. Most of what you'd want to replicate is easily done without needing to restore a whole backup.