Depends with whom I'm traveling. With my young kids, DLH! We like the Disney feel, larger rooms, and used to prefer the grounds but haven't been there since the pool reno so not sure now. We always see characters at DLH (Goofy, Mickey, Donald) walking around in the lobby and outside.
Also, we like to eat at RFC as a family. It's very convenient from DLH. I also like Compass Bookstore (just next door) for coffee and morning treats, and LOVE Jazz Kitchen beignets in the take-out part. We also love breakfasting at Steakhouse 55. I'm eager to try out the new additions, particularly Tangaroa Terrace or whatever the Tiki-inspired restaurant is called.
I like that they have free coffee and 1/2 and 1/2 in the lobby of each tower in the morning.
Finally, at DLH we almost always get our tower choice (Adventure Tower, closest to DTD) so the walk is no big deal. We rarely get our choice in GCH, which makes the walk actually longer than DLH due to the layout of the hotel and lack of elevators.
BUT...when it's a girls only trip, I prefer GCH! It's a more adult hotel and you do feel kind of special when you stay there. With all adults, it's fun to have a drink by the fireplace, eat at Napa Rose, grab a Haagen Dazs, breakfast at La Brea's, hang out in the hot tub and be so close to CA. I don't usually find it a lot closer to DL than DLH due to the position of the rooms, but if feels closer because the hotel entrance is right there. And if I get a really good rate, I love doing concierge for the full-on splurge.