Well....it depends on a lot of things! First, what rates are you looking at for both hotels? Second, what do you like in a hotel? Third, if the hotel is just a place to sleep, why not try a Good Neighbor hotel?
I have to tell you that I almost always opt for a resort hotel, but I'm NOT a "hotel-is-just-a-place-to-sleep" person. I want the atmosphere, goodies, and onsite amenities if I can get them. But I do understand that not everyone shares that opinion and if I did not care about it myself I'd happily save my money by staying off site.
I personally love the DLH and would most often choose it over GCH. Why? Because (a) it's cheaper, (b) it has more of a Disney feel to me, (c) the rooms are bigger and brighter and (d) I like the eating and shopping options better. I also prefer the grounds. GCH has the most awesome lobby, but the rooms aren't better (IMO). You are likely to get saddled with a room that requires a huge amount of walking to get anywhere, which takes away the advantage of being closer to the parks. GCH has the big advantage of the back entrance to DCA, but again, if your room is in one of the back wings it can take about as long to get to that entrance as it does from DLH. DLH has the monorail, which while not exactly onsite is only a very short distance away. DLH has a more welcoming feel and you can pop down to the lobby of any of the towers for free coffee in the morning (better than the stuff you can make in your room). If you want to go concierge, the price is MUCH better than GCH.
Occasionally, though, I like to stay at GCH but I can't exactly put into words why. I think it's kind of a snob appeal thing. I think it feels fun to stay in the ritziest hotel, which defies any kind of logic but there you have it. It's a great place for a romantic time because it's more geared for adults than DLH. The Hearthstone Lounge is a great place to relax, have a drink, and talk. There is a fireplace there and it's cozy with nice chairs, sofas, and even games. You can also go into the main lobby with it's giant fireplace and enjoy the atmosphere there. I like to run over to Haagen Daz and get a sundae which I bring back and eat in front of the fireplace

.
So...it basically depends on what you're looking for and how much you want to spend to get it.