I don't agree. When Universal opens Diagon Alley and Orlando is flooded with tourists, Disney will be

, because a large majority will also spend $$ at WDW. When Disney expanded Fantasyland and brought more tourists to Orlando, Universal was

, because that meant more tourists also worked in a visit to Universal. They might not be working together, but they obviously profit from each other's successes (as does all of Florida). Attendance is up at Universal due to the hugely popular Wizarding World, but not at Disney's expense. Attendance is up at Disney also.
I don't see either park rushing to finish their respective projects just so they can beat the other one. Both parks want their newest attractions open as soon as possible to capitalize on the summer crowds, obviously. I've read several posts on different websites trying to turn these new attractions into a race between the parks. I just don't see it. I doubt very much if the Heads of either park are glued to their windows with binoculars.
Disney doesn't have to "try to steal the thunder" from anyone. Attendance is up, profits are up, stock prices are up, and shareholders are happy. What Disney is doing works, and I don't see them reacting out of fear to anything another theme park does.