Don't forget, you if your HDTV has a digital tuner (also known as an ATSC or OTA tuner) you can put up an antenna and get the best looking HDTV for free. (Note: you will only get broadcast channels, so you can't watch the Astros this way except when they're on a FOX Saturday broadcast.)
Any HD is an order of magnitude better than SDTV, but there's also a matter of which HDTV is the best. It comes down to the amount of bandwidth.
OTA ("over the air"-broadcast TV) has the most bandwidth, and it looks the best, followed by HD over digital cable, then Dish Network, with DirecTV (heaviest compression) coming in last.
Available bandwidth also affects the number of HD channels. Keep in mind that both satellite providers have far less bandwidth to work with than cable or OTA. DirecTV has increased compression so they can provide more channels, and DISH will eventually do this too. For now, DirecTV has more available bandwidth for channels and DISH's offerings look better.