I love both hotels. I've stayed in DLH many, many, many times and have never had a dirty or shabby room. Yes, it is an older hotel and there are sometimes quirks (as with the plumbing), but there is so much charm! The CMs have always been very good to us there. You just can't beat the grounds and the onsite activities of DLH or GCH.
For the age of your girls, I think the GCH would be the preferred hotel. However, I would also suggest that you look into a king suite at DLH in the Dreams tower. The rooms are huge and you'd get the big bed you want. You can also get a prime view of DTD with a great location for accessing the monorail, DTD, RFC, and the coffee shop/bookstore. It may or may not be a longer walk to DL, depending on where your room is in GCH--some of the rooms there are quite a distance from the lobby and though the hotel itself is close, some of the rooms are not!!
GCH would give you a better location for CA and the central part of DTD. It would appeal more to teenagers, I think. If at all possible, you might consider concierge--their lounge is amazing and the girls would LOVE it. There is food and drink available all day long, as well as a computer station and other entertainments. My girls are only 6 and 8 but they loved being able to run to the lounge and hang out a bit. However, the cost is high for that privilege! I think it's $150/day on top of the room cost.
If you decide on GCH, consider asking for a daybed room, as they are larger. I think they only come with 2 queens, though. I don't think there is such a thing as a room with a king and a queen or 2 kings.
BTW, handicap-accessible rooms are larger and/or have more room for maneuvering. I don't know if you can request one of those. Also, there are only a limited number of king rooms and those are generally saved for handicapped due to the maneuverability issue. The king suite would be an exception, I think.