Depends how many cities you have, who it's currently allied with etc. Personally I'd much rather have city-states allies (or friends) than conquer it, unless I'm going for domination.
The Authority / Fealty / Imperialism AI and players usually want to take the cities and are somewhat going for domination. The AI on the current patch is impressive. I played a game on Emperor where Sweden took 26 cities and controlled 4 capitals.