Satalite dishes

Dome:
DirecTV:
No HD programming but works with multiple receivers, DVR's or the Genie (with a bit of added hardware).
Dish:
Full HD available but restricted to viewing programming from 1 of their 3 satellites at a time. This can cause problems if you use multiple receivers or a DVR. Can never be used with a Hopper.
Both suffer from rain fade (loss of signal during storms) more often than an open face dish and can lose signal during heavy dews as well.
Open faced dish (Winegard Trav'ler most likely) has no restrictions and works exactly as Dish or DirecTV antennas mounted on a home work.

What Dutch said.
We had a dome and replaced it with a Trav'ler. The Trav'ler is a larger dish - we have had better luck getting reception through trees with the Trav'ler over the dome.
We have two receivers and both can access any of the satellites at any time. With the dome, the second receiver can only access whatever satellite the primary receiver tunes in. If the primary receiver changes to a different satellite, the secondary loses what ever they were watching.
With the Trav'ler, we can have a hopper and joey rather than just having the 211s. This allows us to DVR any show we want to watch later without having to worry about what satellite is tuned in.
With a Trav'ler there isn't a delay when changing channels on different satellites. This allows us to jump from one channel to another without pause. Of course, the Hopper allows us to view multiple channels at once - great when there are two sporting events on at once.

Which sat service, Dish or Direct? And which receiver model? The domes are only capable of receiving one satellite at a time, while the open dishes can receive multiple satellites at once. That's an important difference if you have multiple receivers or a receiver with multiple tuners and want to watch or record programs that are broadcast on more than one satellite at the same time. For Direct, the domes also limit you to standard definition (SD) only, with no high definition (HD) reception.