Funny, because I was thinking of a Sentinel article from a couple of years ago when Wizarding World was first announced that had the $300 million figure. I did a Google search and found several sources that reference a $300 million budget but I have too much dignity to rely on Jim Hill as my publicly verifiable source of this information.
Wizarding World speaks for itself and it speaks for a hell of a lot more than $200 million. I'm not even sure the ride itself came in at under $200 million. The ride vehicles themselves were easily north of a million each and they have nearly 40 of them. The building materials, landscaping, ride hardware, costumes, lighting, everything was built with first class custom made materials. This is a departure for Universal, which has been notorious for using cheap vendors to get the job done (ROCKIT!!!!!). Everyone seems to think that the average E-ticket ride costs $100 million. That's incorrect. That's how much an E-ticket ride cost to build 15 years ago. Inflation has greatly increased the amount of capital needed to get a ride up and running.
Lastly, just because Disney blows more money on attractions doesn't necessarily mean they turn out better. On paper Expedition Everest's budget dwarfed Revenge of the Mummy's, yet pound for pound E:E's experience isn't nearly as immersive, nor is the story even remotely as well executed, as ROTM.
Who knows. I think they really expect the Fantasyland redo to recapture any market share they might lose with Potter. Even if it doesn't you're looking at 1-2 years before they even green light their next big project.
However, Cars Land at DCA does compare very favorably to WWOHP, both in budget and scope. That more than anything else will be Disney's response to Potter, but only from a bragging rights perspective.