I've got no deep reasons for avoiding Universal, don't have any hatred for it, am not threatened by it, and certainly don't have anything against folks who go there and like it. It simply comes down to not having any desire to go there. I'm not excited about the 'studios/Hollywood' theming of the main park as it just isn't anything that entices me (I also do not care much for Disney's Hollywood Studios), and I have no interest in the roller-coaster/action-ride -centric park either, as those rides are not high on my priority. So for me, there is no primary draw to Universal...but I can certainly understand why there'd be a draw for other people.
Still, I have been to Florida's Universal once for Halloween Horror Nights, and had a fun time with friends...and to Islands of Adventure a few months ago for a business event there in the evening...but mainly just listened to the live music and ate the food provided by my company...I wasn't interested in any of the rides. I have been to California's Universal several times, and stayed generally entertained...but never felt a big draw to the place.
Disney hits on many levels for me, that I haven't gotten from other theme parks. Primary on that list is the theming, the attention to detail, and the immersive quality of the park sections, right down to the design of the posts, types of plants, design of the buildings, posters on the wall, etc. It is truly a full immersive experience that I thoroughly appreciate. I'm probably rare in that I really don't have any connection to any of the Disney character tie-ins, as I don't have kids and don't go to the parks to see movie-themed stuff.
I also love the size and scale of Disney, with even the resorts being like full destinations on their own - with theming, landscape, and architecture that are simply stunning. And with lots of natural surroundings including woods, swamp, lakes, and rivers - some which are left alone and others that are included into the landscaping or used as transportation modes - Disney truly lives up to it's 'World' designation.
I also feel that Disney's parks have a more significant capability to handle 'deluxe' vacationers...the parks have more off-the-trail rest spots and quiet areas, the restaurants throughout have everything from counter fare to formal-dress 5-star restaurants, and some of the resorts feel more removed from the 'theme park' ambiance with their scale and design. Other theme parks are usually more like the original
Disneyland...hemmed in by city life, crammed into smaller space, and with all of the theming being focused on the theme park that serves as the heart. Disney World is rare because it doesn't have just one heart - it has many, with each park and each resort its own entity capable of standing independently.
And of course, the fact that I've been going to Disney since 1971, before there were alternative theme parks there, and have developed a comfort and connection to the place, plays a part in my decision as well. I have the same types of connections to going on cruises, and winter vacations on North Carolina...both things I've been doing for a long time that have become a part of my routine.
I don't think it has much to do with being 'American' either...I know plenty of EU Continentals and Ukers who find Disney World to be a primary draw to the area, and don't have any special draw to Universal. And I know plenty of Americans who are die-hard Universal fans with little or no interest in anything Disney. Being a dual citizen Brit/American...I find both sides of me just happen to enjoy going to Disney World.