It is my understanding that an RV specific covers, such as made by Adco, will not harm the camper. Mine hasn't suffered any abrasions, and we've had some pretty high winds already this winter. Tarps, on the other hand, will definitely damage your camper.
However, if you are looking for something with a waterproof material for the roof, I don't think any of the RV covers do that. I know mine allows rain to pass through (albeit slowly), then it dries very quickly.
Our latest snowfall demonstrated that the cover also prevents snow from being driven into the A/C housing, etc.
I also am confident that my TT is being protected from UV exposure, bird droppings, and leaves.
Indoor storage is obviously the best way to go, but I think the cover is much better than a tarp.