I have had Dish forever. I also had DirectV for a few years and my brother has them right now, and I spend about as much time on satellite TV forums as prime.
The Dish HD DVRs (722) are refined and work very well, their newest 722k is good but not as proven, I will speak to the 722. The interface (UI) is intuitive and quick. The box allows simutaneous viewing of HD programming on 2 separate TV (same program), one via component and one via HDMI, and can send SD via RF or composite cable. It can record 3 shows at once (2 via Sat, and 1 via Over the Air, all in HD), and output a recorded show, and it can also do side by side (POP) of any 2. For a $50 activation, one can add as many external hard drives via USB, to archive (and replay) recorded shows in excess of the internal DVR (25 ish hours HD, 300 SD). Both the NFL Sunday Ticket and MLB are not offered, as they are exclusive to DirectV.
The DirectV DVRs used to be (and will again soon) be produced (OS wise) by TIVO, but the current models were developed in house. Their UI is OK, not as intuitive as Dish (in my opinion), and the boxes are not anywhere near as quick and responsive as the Dish units. Press a button for "guide" and the guide appears a couple of seconds later. From what I've seen the units are fairly stable. They do not support POP or PIP, but can record 2 simultaneous shows (no OTA).
The Dish satellite dish is a bit smaller than DirectV, both (standard with Dish, optional with DirectV) now use bandstacking so that only 1 coax is needed from the external switch (on the dish with Dish, separate with DirectV) to the receiver. HD selection is about the same, both have most of the same channels, each have a few the other doesn't offer. DirectV dropped Versus from their lineup a few months ago, Dish added it free for 90 days.
Dish corp is a smaller, homegrown company founded by a "door to door" big dish satellite salesman Charlie Ergen, and DirectV is currently owned by Liberty Media, a much larger corporation.
Ask any questions you may have, I will do my best to answer.
Miner