Nostalgia is a strange thing, and it all depends on your age. I feel that Disney are losing their crown for this the more new generations come along. Disney used to re-release their animated classics regularly, but that no longer happens, and the parks are actually losing touch with the classics, in my opinion.
There are so many classic properties that are unused, or very loosely used, such as Mary Poppins, The Jungle Book, Robin Hood etc etc etc - instead Disney's acquisition of Marvel & Star Wars has created somewhat of a mixed bag - the parks are no longer Disney, they're a hybrid of all kinds of things.
Take Star Wars - Galaxy's Edge looks amazing and any Star Wars fan will drool at seeing The Millennium Falcon - but for many they want to see Darth Vadar, Yoda, Leia etc....that's where the nostalgia would kick in - can you have nostalgia for 3 films that are less than a few years old? In the future yes, but no presently.
With Universal people are attracted to the attractions as well as many of the I.P's - Harry Potter will always be a crowd puller, and with immersive areas the books/films have been brought to life in incredible detail. Nintendo also has generations of fans, as do the classic Universal Monsters - and Dreamworks have created some magical films that are still hugely popular.
So I feel that Universal is creating new experiences but with a solid basis for what fans love, whereas Disney are not quite sure what their IP's are anymore, they seem to have no real direction or long term plan, which is such a great shame considering what they have meant to people worldwide for so many years.
Disney is nice, family friendly but very expensive - Universal is newer, more exciting, listening to customers and pushing the envelope for theme park experiences.
Also, Disney takes so long to create new experiences - look how long Tron (a clone ride) took to build - and then compare it to how quickly Universal have created
Epic Universe - an entire new theme park....with many rides testing already.
I feel that Universal have a real passion for getting people excited, whereas Disney are just laying back hoping that people will continue coming.