Dish uses 3 different satellites.  Your Trav'ler could "see" all 3 satellites at the same time with the multiple LNB setup.
The dome style antenna have only 1 LNB inside and the software must move that 1 LNB to point to the satellite where the programming is located.  That means that as long as you are only using 1 single tuner receiver you will not have any problems.  However, if you want to use a DVR or more than 1 receiver you will likely run into conflicts when 1 receiver wants to view programming from the 119 satellite and the other wants to view programming from the 129 satellite.  With only 1 LNB under the dome, this is impossible.
As long as you are happy with a single tuner receiver (even with the added hard driver and DVR function) then the dome will work just fine without issue.