I've had both D and Dish since 1998 because they each had something that I wanted that the other didn't. Still true today, e.g., Dish has Travel HD, Dtv has FXHD. So check to see if the channels you want to see are on one service and sign up with them.
But if the programing is the same, then you have to look at hardware. Same story here, each has features the other doesn't. If I had to choose 1, it would be Dish - I LOVE their DVR because of the PIP POP feature. I can watch one program, freeze it, switch to the other tuner, watch a program on it. Freeze it, swap back to program one, jump through commercials until I catch up to live TV, freeze it, go back to the other tuner, play it and skip commercials until it catches up, freeeze and switch back Etc, etc. Eliminates "dead time" such as half time, commercials, etc. Basically "live" dvr without scheduling a recording. this is much better to me than trying to watch 2 channels at once using PIP/POP. And, probably unlike your TV's Pip/pop feature, both pictures can be HD. D has two tuners, but no PIP/POP and can't do the above.
Also if you want to watch your programing online, Dish's purchase of slingbox is producing some really interest capabilities in using the internet and computers to view or manage you programing, but this is not of interest to me.
John W