Think pre-80s city fans bear no ill will towards the county with many, in my experience Cardiff based supporters, often going to Somerton to take in games relatively frequently. Post-90s supporters probably have a similar viewpoint, except they likely didn’t go to any games there when they were bobbing about in non-league.
I do understand city fans coming of age in the 80s thinking of them in a different way. If both clubs played each other more frequently over a few decades I think this fixture would eventually eclipse the city/jacks as the South Wales derby for most supporters, save for the Neath/Port Talbot bluebirds.