The tab at the top of this page for The List shows you all the channels you can get FTA, and which satellites they come from. You can also click on the subscription list, which will in general give you a different constellation of satellites. Receivers built for FTA reception will not show you subscription channels such as those on Dish Network. Likewise Dish Network receivers are not designed for FTA use, even though they might be suitable with different firmware.
Bottom line: the dishes point in different directions, and the receivers are different. Therefore keep them separate.