Domes are probably somewhat less prone to wind damage in high winds.
Domes from what I have heard tend to loose signal faster in rain.
At least with DirecTV domes cannot get HD programming. Since your going Dish that is not an issue.
For our use, we carry a portable dish and tripod plus have the roof top mounted automatic dish. Many places we go the roof top is simply not an option. If I were doing it again, I would forgo the roof top automatic anything and strictly stick with the dish/tripod setup. Using the proper tools finding a signal is not hard nor time consuming. Plus the dish is far less expensive than the Tailgator or roof tops.