This is largely unknowable, but my potted theory is that even if Universal was as aggressive with discounting (and marketing those discounts!) it would still have performed worse than Disney. The theory being that Disney's immense brand cache means that, even with the opening of Epic Universe, the mouse is still the first choice in Orlando ... and I don't think it's that close for most families.
No doubt, especially 'families'. I enjoy the Universal resort experience more than Disney, but more so for the proximity, the Loews hotels, and CityWalk being so close together. I'd say Universal parks have better high thrill rides than WDW....but overall, personally, I enjoy the WDW parks more.... the IP's, the attraction diversification, shows etc. And, I'm about as pro staying at Universal as you can get. So, yeah, Disney is more popular. But I also think Disney management is better. I love Universal, but so many of their decisions at Orlando baffle me. And once they latch on to an attraction trend, thy seem to milk it too long, and their park balance suffers. Damn it Universal, diversify, and build quality indoor stuff, not so affected by Orlando's erratic weather. And get off the need APPs for everything and anything kick. Society is already getting less enamored with that. Even WDW is ;earning their lessen on too much of that turning guests off.
But I do think Universal has to get off the thought process that Epic has, and will, cure all their ills. Nice beautiful park, but not the game changer they anticipated, especially with all the terrific WDW attractions coming in the next four years. . More like when AK opened. Just another park, and a way to extend some tourist vacations. Even someone like me, that'll have had 4 long Universal vacations on the last 12 months, will probably switch a lot of my vacation time to WDW, and cut lots of the Universal time. Universal is just not building stuff I care much for.