Malc, I certainly wouldn't place the rivalry between Dundee and Dundee United in the world's top ten. Matches between the two are, as you would expect, pretty intense but there is nothing like the bitterness/hatred you see in Old Firm derbies. I'm pretty sure you could find a dozen derbies in South America that are ten times as volatile.
Aberdeen are unpopular, full stop. They have a nasty sub-culture of "casuals" and an arrogance about their team that hasn't been merited for 30 years.