I've got a confession to make on this. Myself and a fair few mates have had far more grief with Everton fans down the years at matches than we have with Liverpool fans and as such we always disliked them more. There's generally more of an edge to games between us and Everton which reached it's zenith around the time of the Lescott transfer, and there always seems to be an incident every time we play them at home, even as recently as this season when 2 Evertonians got outed in 110/111 and got escorted out but not before they'd taken a few digs (to their credit, they were still playing up to the away fans as the punches were raining in on them!). However, when you think about it it's not actually that surprising that it's been like that. After all, Everton's main match-going support will be made up of of local working class people as will ours, and then when you factor in the general Manchester/Liverpool rivalry it makes for a potential powder-keg. Liverpool, on the other hand, have a far lower percentage of local working-class match-going fans and Anfield is like a tourist attraction on a match day. It's diluted as fuck.
Now that we've been in 2 recent title battles with Liverpool, my views of Everton and Liverpool fans has changed dramatically. While I think City v Everton games will continue to have an edge to them, I honestly think that if we were in a title battle with Everton that it would never be as toxic as it has been with Liverpool as they don't have the cult-like mentality of their neighbours.