I like both.
Civ 4 is less detailed, easier to intuit. Full game playable in a (longish) day.
EU III has lots of micro management options for when I’m in the mood, the different nations somehow feel different, but it’s sometimes frustrating when I can’t figure out why I’m not winning any battles. Also, not generally playable in one sitting.
Does EU encompass any non-European civilizations?
Yes, you can play as China (whatever dynasty that’s called), Japan, the Inca’s, and so on.
The non-Christian and non-Muslim nations have some type of penalty or other to various tasks, like colonizing unclaimed territories, or incorporating populations of conquered provinces (more unrest, I think). I can’t remember what else, but it can push some players into playing a European power more often than not. (Religion was a powerful cultural identifier, and this is reflected in parts of the game.)
There is also an overall game difficulty setting in the options, so setting that to easy-peasy mode can help mitigate the negative effects of trying to run a pagan country.
I prefer Paradox strategy games to Civ games, but they’re both a lot of fun.
The Civ games are more “gamey”–fast-paced and well-balanced. Like a glorified chess game. The variety is in the randomness of the maps.
Paradox games are better for “counterfactuals”–can I unify Germany, or Scandanavia, or India? Can I prepare the Incans for the inevitable invasion of Europeans? Can I make Korea a regional power? Games are like warfare: long stretches of boredom punctuated by briefs moments of intensity.