Both companies struggle to give you your local HD channels without an OTA antenna but things are getting better. They have many markets available and you can use a tool on their respective Web site to see if local channels in your area are available in HD. If not, you can still use an antenna that attaches to the satellite dish to receive your locals in HD.
Advantage: DirecTV. This is a no-brainer. Not only does their HD package cost less, it has almost twice as many channels.