First, Understand I have a dome, A very good dome (Motosat T-2 Automotion DP)
Now, My advice is this..
If you need IN-MOTION operation, the ability to,for example, record the wife's soaps while you drive the rig down the road to the next campground... THEN you basically have one choice,, a DOME. and one choice of service DirecTV standard
If you want Dish Network the dome can see one satellite at a time, Some domes can re-point quickly (some can't) and thus will work with a SINGLE dishnetwork receiver, both "Standard" and "High Def". however if you have a multiple input DVR or multiple receivers.... You can only watch one satellite at a time.
If you want DirecTV HD.. Domes are NOT an option
Dish type antennas have greater gain (at least 3db greater, often more) and better bad rain/snow performance
They are, however, as Ned pointed out, more likely to be damaged by a high wind.
My dome has been hit with 100MPH winds... I've had dishes up in some serious winds too but they were tripod mounts.
No matter what you put on the roof.. in the line to the receiver put a cheap manual A/B switch, it can be high isolation or standard (don't matter since the unused line will have no signal on it) but just a cheap switch, one per input.
The common lead goes to the receiver LNB input.. The "A" lead goes to the roof up (A)bove, and the "B" lead goes to a connection located down (B)elow, either a through wall (Bulkhead) fitting or a ground block in the basement (Mine is under the hood on my gasser, up on the mounting brackets for the brake master cylinder, easy to connect to and out of the weather)
That way if you are parked under the famous evil signal eating tree...... You switch to "B" and use the ground mount.