DirecTV does technically have the best HD PQ. But they also have the worst SD PQ, and several channels in SD that Dish has in HD. As the previous poster said, the HD PQ difference is barely noticeable, if at all. The part-time business is technically true, but very misleading. Several regional sports channels are broadcast only part time on Dish. Makes perfect sense, to me, but DirecTV makes it sound like Dish randomly shuts off all their HD channels, which is completely false.
Having had both, I can tell you that Dish's HD PQ is excellent and that they have a lot more basics in HD (BBCA, TCM, E!, G4, DIY, H2, etc.), basically all the HD folks have been whining about D* not adding for years. If you like expensive sports packages, full-time regional sports off-season, PPV, lots of basic content in dazzling SD, and painfully slow DVR's, then DirecTV is the provider for you.