I don't think he does. I like him and think he was really good for us, but I think people exaggerate his actual influence. He wasn't the physically imposing figure Rodri is. He wasn't as fast in recovery and could easily be bypassed if not surrounded by legs around him. He wasn't as press resistant as people like to remember, and due to his natural pace of play, wasn't a quick distributor, even out of pressure.
Rodri is all of those things, which is why he is considered the best midfielder in the world at present. So its not a knock on Carrick, but he just simply wasn't near as good.