I've been somewhat disappointed in the past, because the challenge of playing on the higher difficulties comes less from a smarter AI opponent and more from the handicaps given to the player. For example, on Deity, your base happiness is lower than the AI's, you start 5 techs behind, you pay up to 2x the price for routes, buildings, units, and so on: (http://civilization.wikia.com/wiki/Difficulty_level_(Civ5)).
It definitely forces you to play smarter, but the AI seems to more or less play the same way on King and up. I'd be really interested to hear some commentary on difficulty level and AI tactics!