Closed. Visor down.
I raced for many years and it only took one incident to convince me. I have always had a closed-faced helmet, but ran with no visor, or visor open. Then during one session, I had the visor partly open, on the front straight something pinged my visor right at the edge of the opening. After the session, I found a pen cap in the footwell.
Had I not had the visor it would have hit me square in the left eye. At about 110mph. So, yeah, full-face and closed.