The only other thing not mentioned that I would add is that Hyatt has some great promos for earning points - the G bonuses were mentioned (although those seemed to have disappeared nearly completely now that they offering 10K bonus points for every 5 nights) - plus they also do some good free night promos - stay two/get one free. I also think that the redemption levels at Hyatt are generally lower as some perfectly acceptable properties are available for only 8K per night. I don't think you see those levels at Hilton or Marriott.
I do think however that the lack of properties in lots of areas of the US that others have mentioned is a MAJOR drawback. Hyatt should have at least one option for travelers and vacationers in Maine, New Hampshire and Vermont.