Just going to add my two cents here since I've had both in the recent past. I think the difference in PQ can vary widely between the two services. These are my observations with Durham, NC locals. My primary TV is a Sony XBR70X850B:
1. Neither is as good as it should be. Both exhibit an odd judder from time to time which I could never eliminate. I don't see this on other sources, so it must be something to do with the transcoding the satellite companies do. Comparing to OTA, they both look subpar.
2. My local channels look a bit better on Dish than DirecTV.
3. "Standard" Cable channels (TBS, ESPN, etc) look noticeably better on DirecTV than Dish, at least to a critical eye. A casual viewer might not notice.
4. Premium Cable channels look about the same on both. HBO/Cinemax might look better on DirecTV now that AT&T owns them, but I don't know -- that is just something I thought might happen.
5. I did recalibrate my TVs after I had both services installed. They do look different from each other in raw form, so, if you really care about a good picture, you have to work for it.
6. It seems like there may be some variability with Dish depending on which satellites are used. I am on the Eastern Arc satellites. It seems to me that most of the people I see complaining about PQ on Dish are on the Western Arc birds, but that is just my impression.
Outside of picture quality, I prefer Dish hardware, features, customer service, and channel packages, but I can see why someone would prefer DirecTV if they have different priorities than me.