I play mostly single player for the simple reason that it's difficult to get a proper multiplayer game unless I organise it with a friend in advance. The vast majority of the multiplayer games are tiny, quick speed games dominated by early rushes, and never make it much beyond the classical age. This is only a fragment of a full Civ game, and doesn't interest me. I like long games which take in the full tech tree, and where I'm not being rushed to complete a turn in 30 seconds flat. It's not as if it isn't possible to save part way through a long game and continue later.
A human player is far more of a challenge than the AI, and in many ways more fun, but unless I arrange a game with someone I already know no one seems interested in a game which lasts more than an hour. Therefore I mostly stick to single player.