Both can happen, and have. I tend to see Disney and Universal parks as comparable, all things (except personal nostalgia) considered. Disney is slightly better at some things (e.g., immersive and beautiful lands, varied ride systems), and Universal at others (parades, roving characters, street entertainment, and holiday/food festivals. Further, the vast size difference between the two results in obvious advantages and disadvantages for the two resorts, but again, in ways where the pros and cons generally even out. (e.g., Disney can spread out lands, offer more parks, and rely less on screen-based attractions, but Universal's smaller footprint makes navigating between the parks, CityWalk, and hotels, effortlessly quick and convenient).
*Personal sidenote: Where the dealbreaker difference lies for me and my family is not in the quality of the parks/hotels themselves, but in the logistics of a park visit -- and in that area, Universal offers a far less stressful and more spontaneous planning and visiting experience, without the need for multiple layers of upcharges or spending vacation time staring at my phone. I really hope that the opening of Epic Universe (with details about ticketing, pricing, etc. yet to be released) doesn't alter the equation in a negative way, and that Disney at some point comes to understand that it will be a far more attractive destination if it can streamline and "unplug" its queuing systems, and redesign its queues to eliminate the visible caste system that has made the waiting experience so demoralizing.