Yes, HD off-air will look better and probly sound better too. Of course, it's also subject to the quirks of broadcast reception, but it either works or doesn't. If you get a decent signal strength it's great.

The satellite boxes do have HD tuners in them, you just hang a UHF antenna off the dish and diplex it in on the sat cable. If you want lots of HD channels, Dish Network is the only real option. The Dish boxes do not have analog tuners in them though, just HD. Not sure about DirecTV.