I never know how to answer this. I love both hotels. I prefer the rooms at DLH and I like its simplicity. By that I mean that it doesn't twist all over the place--everything is laid out nicely in a way that makes sense. GCH is a little bit of a maze IMO. I like the grounds at DLH better but the lobby at GCH is a really nice place to hang out and is close to places in DTD I like (Hagen Daaz & Marcelines!). DLH is also nicely located next to DTD and is very close to RFC, the monorail, and used to be Compass Bookstore. Rumor has it that Compass is going to be either Starbuck's or Earl of Sandwich--I haven't kept up on what the latest news on that is--so that's nice, too. And I LOVE Trader Sam's! The DLH gift shop, as a PP mentioned, is superior to the one at GCH but then GCH is right next door to World of Disney.
The upshot is, each is fabulous in its own way. I think a lot of people prefer GCH, without realizing it, for the "elite" factor. Honestly, the proximity thing is very minimal IMO. You add maybe 3 minutes by staying at DLH; if you have an outlying room at GCH, the walk to DL is no shorter. It is a nice convenience to have the DCA entrance, though.
See...no help from me!! I've stayed at both hotels numerous times and I still have trouble picking one when it's time for a trip!