I was a GCH only gal until I stayed at DLH for the first time in May. Now it's a complete toss-up! So I suppose it's what's most important to you.
Overall I found DLH to be lighter, brighter, and funner. There are many more Disney themed touches all over the place than GCH, which I LOVED. Teacup chairs in the lobby, the giant map with animated parts, monorail pool, and the light up sorcerer Mickey hat you walk through on the way to and from the park all really make the stay feel more "magical". I liked the rooms in DLH more as well (though I wish they had balconies). they felt a little bigger, and the bathroom layouts are usually better. Not to mention how awesome the light-up headboard is that plays music (even my 12 y/o loved it). Overall, I feel you can't go wrong with the DLH.
The GCH on the other hand, has some distinctive perks in my eyes. It's darker and cozier than DLH, and you get the sense you're at a laid-back, far-off retreat even though you're closer to everything than DLH. The lobby is awe-inspiring (much like Wilderness Lodge, I hear, but less floors) and when you first walk in there's a definite "wow" factor DLH misses. Everything is just a bit nicer than DLH when it comes to the common areas, especially the elevators, which are bigger. The rooms feel more compact to me, but have cool lanterns that dim, and the best part is the balcony and the view (aside from standard you can get quiet courtyard w/monorail going by, pool area/Cal. Adventure, or Downtown Disney [my fave]).
I usually save GCH for the Holidays, and would like to use DLH for summery/spring visits, but that's just me. Good luck on your decision!