Hi Fulltiming,
Welcome to the RV Forum. It sounds like you'll be traveling all around the U.S. and probably Canada. That being the case, DirecTV will have an edge. As an RVer you will be able to subscribe to east (NY) and west (LA) coast feeds (you'll have to provide relevant RV information to get it). You'll want this if you're on one coast or the other because of the three time zone changes and to get weather reports closer to your actual location. This is not available on Dish. Additionally, if you have both feeds you have the added advantage of seeing shows on either channel at a specific time. This is good when you have two shows you want to see that are on at the same time (watch one at 6 and one at 9). Now someone has mentioned TIVO which will negate this problem. If that's what you want, fine. We prefer to watch shows when they're on and not have them stack up to watch later (kind of like having several VCR tapes stacked up) so we've never gotten TIVO and don't want it. Each to their own...
The other primary difference between DirecTV and Dish is that Dish "may" be more sports oriented (it used to be but I don't know if it still is). In either case, you'll have to look at their list of available channels and see what option packages will provide the channels you want and what you'll have to pay for the various options. A member of my family recently got basic Dish and we think we have more basic channels with DirecTV. Although Dish has given her good service (I've also heard horror stories), she actually meant to call DirecTV and dialed wrong. Dish was unwilling to break her 18-month contract, so buyer beware. We also really like the onscreen TV guide. Once you have satellite TV you won't want to go back to the cable guide which only shows current programs. With DirecTV you can go days out into the future to see what will be on.
As to trees, yes we occasionally have to "make do" with either cable or through-the-air TV but usually we can move a foot or two and correct the problem (we've even changed sites). We often look in the Trailer Life campground directory and see what it says about the sites at a particular campground. If it says "most sites shaded" then you're more likely to have tree blocking issues than if it says "some sites shaded." Some campgrounds have a lot of trees but they're small and the roof-mounted satellite dish doesn't have a problem seeing over them. OTOH, if they're huge old oak trees then you might not be able to get a signal. We've been surprised more than once, either because we couldn't get a signal when we thought we should or because we got one when we didn't think we'd have a chance. When you check into a campground ask for a site that doesn't have trees.
By all means, if you're going to be a fulltimer and can afford it, get the roof-mounted automatic dish. We've had each kind and LOVE the current (roof automatic) one. We have a MotoSat box where we push a button to "Find" or push another button to "Stow." It's SO much easier than the manual thing. Even when we had the manual dishes we sometimes couldn't find a good line-of-sight for a signal, so it's almost a non-issue. The farther north you go (e.g., Canada, Alaska) and the farther east or west you go (e.g., Newfoundland, Alaska) the more likely you are to lose your signal because of the placement of the satellites around the Equator. The curvature of the earth means you simply leave the beam from the satellite when you go too far in one direction or the other. Also, don't forget that you'll probably have more than one TV in the motorhome, one up front, one in the bedroom, and perhaps even one in an underbay. You'll want enough coax cables down from the roof-mounted dish to accomodate each TV that is to have satellite reception.
Finally, because of the upcoming changes in analog vs digital TV signals, I highly recommend getting HDTV-ready television sets. We didn't think we'd see much difference between "regular" vs digital TV, but needed to buy a new set and we really like the HDTV much better. So much so that we now also have one in the motorhome. The pictures are significantly improved. In our local area we can get the major networks in either analog, digital, or high def and when we jump between the same networks we really can see the improvement. So HDTV far exceeded our expectations.
It sounds like you're off to a wonderful adventure. Do check in when you have other questions and let us know how you're doing.
ArdraF