I absolutely love the DLH. I have stayed at GCH (and Paradise Pier too for that matter) and while the GCH is incredible and the details superb, I prefer the DLH. Above all the other Disney deluxe level resorts in both WDW and DL, the DLH has the Disney touches that are tasteful but so fun and whimsical. I enjoy the oversized, light, bright rooms and the pool area is great for kids. I also enjoy the grounds of the DLH, it has some things like the arcade (no arcade at GCH, not a biggie but my kids enjoy burning some quarters) and the remote control jungle cruise boats. I also think the DLH has better dining choices for a family.
You can't make a bad choice but for me, the DLH wins!
I'll also add that I very much agree with Sherry. I enjoy the craftsmen theming of the GCH and enjoy cutting through the lobby on my way to and from DCA to the DLH. I also enjoy eating at Storytellers and Whitewhater snacks. But those are things that don't sway me enough to stay there. I do think the balconies are a great selling point for the GCH, I wish the DLH rooms had them but I guess you can't have everything! I also think a big factor for me and the DLH is the bed situation. At the DLH you are guaranteed a third bed. Either a daybed or a rollaway (rollaways are free there). The GCH has some bunkbed and daybed rooms, however those are request only. If you don't get one, you get a sleeping bag if you need a third bed option. With two teens who can't sleep in the same bed, being assured one of them will have a comfy bed is a big plus for me.
I have never had a rundown room at the DLH but it is for sure older than the GCH. But in seven stays in the past five years, I've been happy with the rooms as far as the shape they are how clean they are.