they both carry local in HD…if you have the HD package along with local you get the local in HD & standard def.
they both have the main stuff, ABC, CBS, NBC, Fox, but to get the others (only a few) you have to get an antenna, WB, PBS, etc…
Dish networks reciever accepts an antenna input & integrates the over the air channels you are pulling in with the dish channel so they are all visible in the guide.
i assume Direct does the same thing.