I have DirecTV and my dad has Dish at his house, so I've used both extensively. I don't think there's any huge features that one has that the other is lacking, other than DirecTV having the NFL Sunday Ticket if you have any interest in Football(you'll almost always get this for free the first year you sign up)
I'd probably just make a decision based on pricing. I know DirecTVs basic channel tier is 140 channels where Dish is only 120, so Dish has a decent amount of channels that you have to go a tier higher than DirecTV to get. I went with DirecTV because it was cheaper than Dish when I priced both(especially for the first year when you can get some referral discounts too)
Also know that the Hoppers(Dish) claim to recording 6 shows at once is kind of bogus, that only happens during Prime Time, and it just DVRs the networks automatically, and you can only choose like 2 more of your own shows.
At my home we have 2 DirecTV HD DVRs(not their new Genie), and we can record 2 shows per box, and each box communicates with the other, so our DVR guides show everything available on both boxes. It can function like a whole-house DVR even though it isn't advertised as such, I'm not 100% sure what the Genie offers that is much better than that(other than the wireless Genie boxes), but they definitely charge you more for it