Civ4 was significantly better than 5 or 6 in that regard in that the computer players weren't so game-ified into sociopathic lunatics that would go from long term allies or trade partners to instant chain-denouncing mortal enemies based on seemingly minor changes in the player's expansion or military strength.
Additionally the ability to stack units, while having problems of it own, made it a lot easier for the computer players to pose any serious tactical threat (without a gigantic technological advantage, a careful artillery and melee formation with a few healing units thrown in can destroy any computer-managed army of even ridiculous size; and the various "cheat" modifiers can magnify that to the point that independent city-states have been observed kicking the tar out of computer-player empires in both civ5 and 6 due to the regenerating free era-appropriate units that the tactical code simply can't out-maneuver)
Multiplayer in 4 tended to be all early rushes and road-ing/choke-ing (get some early unique units or archers to sit on key resources, stealing workers to build roads in between so your units could mass up to take cities faster). Back in the day I had a friend to play intentionally long games over weekends cooped up in the winter, those were immensely fun with a gentleperson's agreement to avoid direct conflict and try to win via tech/culture with maneuvering by proxy. The Civ4 AI personalities were much better suited to this as well.
Never tried MP in 6 but did some co-op in 5 that was reasonably fun, you really had to dedicate multiple evenings to it though so getting more than 3 people was impossible unless you were all sharing a dorm or something.
Overall the most fun multiplayer experience in a Civ-like game I've found was in Age of Wonders 3 as the games had a flatter tech ramp, tactical combat modes that took advantage of the hex map like war-games, and a RPG-light cast of semi-random hero generals to level up and give cute magic items to. Plus it had a variety of MP game modes for both competitive and co-op play.