I think you put the cart before the horse.
Why would you buy a carry out dish before you know what service you will be using. It's like going to an auto parts store and buying a carburetor, than asking if you should buy a new Ford to install it on.
Both Dish and Direct offer a variety of receivers. Different receivers require different dishes/LNBs.
A better approach is to decide which service you want than which receiver you want to use at home. Then what you need to do in your RV to use that same receiver.
I spent 10 years in an RV with Dish for my service provider. 5 of those years were full time.
If I were where you are, I would choose a Dish Hopper 3 system for the house and an appropriate roof mounted dish set up so I could carry the receiver from the house to the RV. Depending on your frequency of travel and where the receiver will be located in the house and RV, you may quickly tire of disconnecting and reconnecting things. Often the receivers are placed in cabinets where you can't see and can barely touch the connections.
You may ultimately choose to have a second Hopper 3 installed in the "spare bedroom "/RV.