Private hospital vs. State/Public hospital

I've held out as long as I can, and I know a visit is in the cards. This has been the worst week of my life.

So I have two options: go to the closest emergency room, be held until a bed is open, then transferred to the state psychiatric hospital.

Or, I could call for an assessment at the local private psychiatric hospital.

Both are in-network as far as insurance goes. What's the difference? Experiences?