For a deep game, I have read that Starbase Orion is a great 4X game. I am hoping to get it once I get my iPad, but it also plays on the iPhone. I believe it has a good amount of depth to it, but I am not sure how similar it is to the Civilization games. Pocket Tactics wrote a good article about how it has become very polished and quite deep (Source).
As an alternative to the Civilization games, Polytopia is quite decent, and would likely be good to play on the iPhone. It is nowhere as deep as the Civilization PC games (never played the mobile Civ games), but is good for a mobile game. It is also free, with extra civilizations costing $1-3 USD each. This way, you can try it and see if it fits your desired depth.