Mavericks Notes not compatible with IOS 10 Notes?
Yes, there's a compatibility problem. Notes were upgraded in iOS 9 and OS X El Capitan, and you can't sync between OS versions from before and after the upgrade. You'll need to upgrade your Mac to El Capitan or Sierra (which you should do anyway, since Mavericks will soon stop getting security fixes, if it hasn't already).

As a workaround, you can use a web browser to access notes in the cloud via web app. It’s not as convenient as the native app, but you can get at the notes from https://icloud.com