iPhone 4 syncing to old version of iCloud Notes, even after reset and on different Apple IDs!
Assuming your freshly-laundered phone was using iOS 9 &amp; your iPhone 4 is still on the last available iOS for it, 7.1.2, then the reason it cannot sync to new Notes is because the new Notes feature was only introduced with iOS 9

Anything older will still be syncing to the older version, presumably last updated the day before you hit the button to upgrade to the new version when you loaded iOS 9 for the first time.