I live on Oahu part time and visit Waikiki often. Not much to add to this thread that has not already been said.
The fact is, as another post stated, they are two very different hotels. You are not really comparing apples to apples. Trump is a very different hotel experience than Hyatt.
My girlfriend is a Trump aficionado. She loves the brand and the properties. We stay at Trump every chance we get (because she insists), and when we visit Waikiki, we always stop at Trump just to have a drink, lunch, spa, whatever. We rarely stay there as we have a place on Oahu.
You'd have to visit both. See which "flavor" of hotel you like. You are going to pay for Trump, but that's part of the brand. You can always stop by the gift shop and buy a "Trump" T-shirt to sport your support!
