I used to have Directv several years ago, before I made the switch to Dish. It's surprising how after all this time, Directv has pretty much stayed the same. Aside from releasing the newer, smaller, faster Genie models, it's still ultimately the same 5-tuner whole-home DVR with the same user interface, so it doesn't really feel like they've done anything new that's been a major upgrade, aside from maybe the few 4K channels which Dish doesn't have.
As far as PQ, people have said that Directv has better HD, but Dish has better SD. Ever since I got the Hopper 3, the SD channels have looked way better in terms of picture quality. Watching Buzzr in SD on my 60" TV looks perfectly fine. And honestly, I'm not much of a stickler in terms of comparing HD feeds, so they look fine to me as well.
The main negative with Dish right now is the recording issues that have resulted as of the switch in guide providers from Gracenote to Rovi. Aside from having to manually set recordings and check the timers every day or two to make sure your programs are in fact being recorded, Dish is still leaps and bounds ahead of Directv. Hardware-wise, you've got the 16 tuners, plus PTAT, which alone solves many recording conflicts in and of itself. Software-wise, compare the program guide and the UI for the H3 with Directv's old-fashioned text-based guide that they've been using since 2013, and you won't ever want to switch back.
Even with the recording issues right now, Dish is still way ahead of Directv, and until AT&T comes out with a receiver equivalent to the H3 in terms of tuners, with an updated UI that's not just 90% text-based, it's kind of hard to justify going with them. Unless you really love sports and the 4K content... but even then, after you've used the H3 for a few weeks, you won't want to go back, seeing the difference.