I don't know that Uni and Disney can directly compete over the same vacationer. I think the person who said both companies compete to keep people from doing a different TYPE of vacation are if not correct, more accurate. Uni and Disney both satisfy two totally different wants from the same theme park visiting guest. Growing up we went to Disney several times a year but once my sister and I were the right age our parents took us to Universal, because what we wanted to do/see wasn't something Disney could reeeeally provide.
For a better example, take a look at their Halloween activities. Disney has MNSSHP, which has some great shows, a parade that's...well it still has a great soundtrack and elements even if some things have been shoved into it...new fireworks, and characters and candy EVERYWHERE. It screams PLEASE TAKE YOUR YOUNG CHILD HERE (or for those of us who don't have/want kids...take your inner child here) Meanwhile at Universal the goal is "we're gonna scare the ever living crap outta you AND YOU'RE GONNA LIKE IT" and for the most part...that represents two completely different types of theme park goers. MNSSHP and HHN aren't competing for the same family. They're each there for the people who don't want to be at the other's event.