The only way Disney could actually eat part of Universals business away is to let the family friendly, snowflake, pixiefarters, overweight princess humping demographic go and grow some balls. It's what Disney doesn't have. Universal already has that part and serves them rides and ip's they want, with their next park I'm sure they focus on the demographic they don't have yet and that is the family friendly, etc. Sure there will be a bit of an edge, it's Universal, but I think they understand what market they want to get next.
Regarding Disney cleaning up their parks, it's about time. DHS, Epcot and AK never could exist on their own and see the numbers they get when they weren't part of a resort. From what I see now they are not on track on doing that successful. AK needs more rides, Avatar only had 1 good one and the total thing costed too much for what it offers, the nighttime show doesn't do what it should. Epcot doesn't need another restaurant, there are enough places to get overpriced bad food, no need for a space restaurant. Placing a Guardians coaster confuses me, sure they slam an "educational light" sticker on it making it even worse. A new lagoon show, it's about time but there are more empty buildings that needed to be filled with meaningful rides first. Slinky dog, downgraded oven that is designed in a bubble. Walt told imagineers to visit the parks, try that first and actually think about your guests as humans. And than there is Star Wars, the only thing that could get me back to the mouse but it's not like Potter from the movies but a Chinese knock off that took some familiar part and threw it together to a patchwork land I don't care about (a DJ in a cantina wtf).
In the end I hope Universal will feel the pressure, Disney sure does, it only makes things better (at Universal clearly).