They are both great hotels, however I find GH a much better deal. The rooms are nicer, the staff is better trained and over all it is a much better experience. Here is a review of the hotel:
http://www.flyertalk.com/forum/hyatt...er-thread.html
If you do not care about points or your stay counting towards elite status, the Hyatt Regency can be a steal using the Hyatt classic certificates - $109 a night, taxes included:
https://www.certificates.hyatt.com/
There were times when weather or mechanical issues have forced me to spend the night at DFW without advance reservations and I had to spend $110 a night at the DFW Fairfield Inn.