City-States with my religion

Does a city-state following my religion lose influence at the same rate as one that does not? Or do I only get the initial bonus for spreading it (if they requested it) and the papal primacy bonus to the resting influence level?

You lose influence 25% slower.

Thanks

In my last game as Greece, I had Patronage opener (I think that's the one) and converted them to my religion. As soon as I got enough gold to buy influence (after getting my 4 cities up and running well), I would get to 70(?) influence and then never having to give them any gold for the rest of the game and enjoy all of the bonuses.