I played AC after Civ 5 and i really enjoyed it. I enjoyed it so much that i even moded it's horrible horrible tech tree.
Most of the OP's complaints about CivBE are valid and i agree with them. AC had a menacing atmosphere as well as a very depressing ambient sound (which was very very fitting). From this point of view AC is superior hands down.
Gameplay wise AC felt unique, but it wasn't necessarily a better experience. It's difficult to explain and to pinpoint it's individual failures, but there are a lot of them. Here is my personal short list of things i don't like in AC: Squares, ICS, tech tree, doom stacks, "clean" minerals, water cities.
Personally i think that both games should be played as neither is perfect.