A clarification: The "upgraded" Notes app only syncs with iOS 9 and El Capitan.
I chose to not upgrade my Notes app data (or any of my iCloud back end) to the new version. My Notes data is still available in iOS 9 and El Capitan, and also on the iOS 9 device - in addition, I'm also presented with an "Upgrade" option in the iOS 9/El Capitan Notes apps.