From a visitor's point of view I have never understood the 'rivalry'.
We have been visiting Florida since 1990 and like Disney AND Universal.
If I had to make a choice as to our favourite park it would be Magic Kingdom because as a family that's what we enjoy the most.
However, the 2 Universal parks come next on our list and every time we visit Orlando we enjoy our numerous visits there.
You will find most of us on the UK forums on this site like both WDW and Universal and the 'rivalry' (not sure if that's the right word), is not as intense.
There is an element on the DIS who seem to look at everything through 'Mickey Mouse sunglasses' and if it doesn't have Disney on it they are just not interested.
Many of the rides for instance at Universal would be raved about a lot more if they were at the Disney parks, such as Spiderman and Shrek to name just 2.
The car parking facilities are also much better - *one of my current gripes being as a disabled badge holder (through our son) you can barely make out the blue lines on the very worn Disney car parks*.
I also think US are much more pro-active in updating the parks and bringing new attractions, something Disney could learn from.
Though there are many reasons Disney has the 'magic touch' being able to stay on-site a short monorail ride away from MK is in theory a great experience we are hoping to indulge in next April.
Sure if you thought long and hard about everything you could pick out little faults and things you just don't like but I think overall the more attractions in Orlando the better for everyone.

If it means more people like us from outside America visit Florida that has to be a good thing surely?