I stayed at Grand Hyatt Dubai first, then move to Park Hyatt this week.
Used Suit upgrade certificate and upgraded to Park suit, which was quite nice and was well appointed. For transfer from Grand to Park, they kindly arranged chauffer service. It was a nice Mercedes S class limousine (lease from Sixt). Other private cars at Park are Lexus, Toyota Land cruiser, BMW. I could not find Mercedes S at the front door area. So, I guess for complimentary chauffer service, they may use a special car and a driver. Within Dubai, hotel private car command 3o-40% more expensive. However the taxi tariff is quite cheap, I opted for private cars. The cost of gasoline is only $US0.3 / litter!!