For me, It kind of depends.
For slow, precision shots, dominant eye only works well, with maybe the other eye slightly open.
For faster shots and / or multiple targets, both eyes open definitely works best then.
It depends on the kind of sights, too.
Optical and small iron sights seem best with on eye.
Large iron sights and dot scopes seem to work best with both eyes open.
Walt Kelly, alias Pogo, sez:
“Don't take life so serious, son, it ain't nohow permanent.”