I don't think you can go wrong either way. It sort of depends on what you're looking for.
I stayed at the GCH with my mom and loved it. It was perfect for us- a bit of luxury, minimal walking to the park (so she could go back and rest while I did screamin over and over and over...), Napa Rose downstairs, and piano music in the lovely lobby.
I did DLH with a small child and loved it. Disney stuff everywhere, great renovated room, fun headboard, and Goofy in the lobby. Plus, she loved taking the monorail.
Both hotels are great, but for totally different reasons. When are you going? That might affect the pool situation at DLH...