Of coarse they're in competition.
Disney recently added the Magic Express Service to take people from the airport to their onsite hotel. Why do you think they did this? So people won't rent the car and drive up to Universal.
Disney brainwashes people into thinking they need an entire week to tour the parks. Most figure a day at each, plus a water park, plus hanging out. When Disney people talk about visiting Universal, they only take ONE precious day away from Disney. In reality, most could tour Disney in 4 days, and then spend 3 at Universal.
Years ago, Disney (Eisner) added hotels. Then it was new shows along with Everest. Universal countered with The Mummy, but now they're playing catch up with Blue Man Group, Harry Potter land, and two new hotels.
The attendance figures tell the story, Islands of Adventure is dropping, even if people are spending more money when they visit. IOA will have the new HP land, and Disney will counter with something huge. To me, it's thrill rides that matter, and it seems they happen every 4 years.