A co-cathedral exists usually when two smaller dioceses have been merged; one of the former cathedrals becomes the co-cathedral. I don’t know the history of the Houston diocese, but I would imagine this is what happened to result in the “co-cathedral.”
That said, I’m not a great fan of these giant “Risen Christ” images. Looks to me like we’re avoiding the Cross.
It looks to me to be a beautiful building which will honor God.