All the notes are tied to an iCloud account, or in the absence of one they're saved locally. If your aren't signed into the same iCloud account on both phones, then the notes won't transfer. They both have to be using iCloud drive, or both using Documents & Data. No mixing and matching on that.

iCloud Drive is the new way data is saved in iOS8. Documents & Data was the old way.

If the notes were entered before you signed into the iCloud account then they won't transfer.

Basically, if you're using the same iCloud account on both phones and both are using the same kind of document storage, then they will transfer. Any other configuration and they won't.