I find that a bit strange to be honest, if Everton were ever in a position like Citeh, of playing fantastic football and totally dominant etc then I'd take every bit as much pleasure out of beating them as Man Utd, hell I take almost as much pleasure of beating them even now! I would have thought that there was a fierce rivalry between Utd and Citeh but perhaps it needs a few more years of them dominating and making Utd into the second bets club in the city.
Basically it's all about winning in my opinion when it comes to rivalry. The more a team wins Cups, leagues etc the more the opposition seem to dislike/hate/ want to beat them. There is a fierce rivalry with City but over the years ( till recently ) it diminish somewhat through their lack of success.
Watching Livepool dominance in the 70s as a teenager it became very easy for me to want to beat them more than City. I honestly believe that's human nature as success does breed jealousy unfortunately.
I'll be no different come Derby day. Hope we smash them and Ole does whatever he's doing now continues.
City will never ( in my life ) be bigger than United nor win anything close to what we've won. Manchester will be red for at least another 25 years before they can even think about passing our haul of trophies.