Of course they do- but the ease of MDE is not an issue- it's incredible. The in-park transportation- while not perfect- is about as good as it could be (with the exception of the new time boards that change every minute to a minute later just adding frustration of when the bus will or wont arrive).
Airport and internal transportation might be managed differently via Disney and Universal- but to the paying customer- they don't care. They just want it to be easy and work. Disney offers that, Universal doesn't. And thats something they can currently fix.
Note- next week I have 2 nights at the Royal Pacific trying to convince my wife how great Universal is before our 4 nights in Disney- she has fought and fought going to Universal because she loves Disney so much. Having a super easy way of transportation would help take the blinders off quite a bit. Of course, we're using a towncar service- but that costs $. If it was similar to MDE- she would be much more impressed.