From what I can tell, Directv seems to have an edge on PQ. I have noticed on the wireless Joey that the picture does have more digital noise on all channels. The Hopper 3 has a good PQ, but I think Directv has a slightly better picture. Of course, this is my opinion. Would it be enough to make me reconsider the switch? No, I have always enjoyed Dish's equipment over Directv and PQ isn't at the top of my list as much as the equipment. I also tailgate quite a bit, and I think Dish embraces the concept better than Directv.
One thing I have noticed is that Directv does seem to have more channels in HD. There are certain channels that would be much more desirable in HD as I feel SD channels are borderline useless. Nothing like SD on a 4K set. Haha