Leona skill order

I am a fan. She is my second most played champ this season by mastery score and in ranked I have a 56% winrate with her (not great, but at least it's positive)

So for skill order, for levels 1-3 it's pretty standard, Q, E, W, then following maxing W.

The question is what to max second, Q or E? Most of the guides say to max Q second, but I prefer E. My reasoning is that the main reason to max either is to reduce its cooldown, and during a teamfight I am more likely to be able to E someone on a second cast than Q them. Even though Q is better for its vastly longer stun, and being a stun as opposed to just an immobilization, as Leona in particular I find it more likely that I will be out of position with regard to protecting a carry than with someone like after burning E, Q, R, etc.

Thoughts from people more op than me?