In my family we have both DirecTV and DiSH Network
Picture Quality (As seen on the same TV)
DirecTV has better picture quality, both the SD and HD channels. The DiSH network picture quality was pretty bad imo but both HD pictures were highly compressed, but DiSH looked worse
DVR
We only have DVR on DiSH, it can hold 50 hours of HD and 400 hours of SD I believe. But the big thing about Dish is that for a one time upgrade of $40 to your DVR you can export anything you recorded onto your computer to free up more space. I dont think DirecTV DVRs can do this
I think the DirecTV DVR can only hold 20 hours of HD, and 200 hours of SD
Contracts and packages
DirecTV requires you to sign a 2 year contract, and if you cancel it early the fee is 5 or 10 dollars for each month that you cancelled early, I cant remember the exact number. If you wait for the right time they will have a sale that gives you all the premium channels (HBO etc) for 3 months free.
When my sister signed up for Dish they gave her Cinemax for 12 months for just 1 penny along with HBO and other channels free for 3 months. I'm not sure about the contract.