I don't think you have to have championship implications to have a great rivalry. You do have to have two motivated fan bases, teams, communities, etc. that live and die for the matchup. I haven't been to most of these games, so I won't comment on which one is best, but I think the championship angle sometimes gets played up too much in these conversations.
The Pisgah-Tuscola rivalry is a case in point. I know folks from both communities, and you are just as likely to hear about this game in the middle of February as you are during the season.
Swain-Murphy is a good example of championships being present but not necessary for a rivalry. I know some Bryson City folks that won't spend money in the town of Murphy for any reason just because they hate Murphy that much, and I know the love is reciprocated. This is a game I have been to, and the tension is fantastic. Both teams waiting for the other to come out of the locker room first just to screw with each other is a nice touch.
At any rate, you can't argue with the number of championships and success in the Crest-Shelby matchup and the implications of state and conference titles will always add drama to a rivalry, I just don't think that is the end all-be all of a rivalry.