I've stayed in both recently, and they are both great. The "themeing" in the GC is better. It has very much of the feel of the WL. It's also closer to the parks, and it's really nice being able to get directly in DCA. Sounds like you have a pretty big group, and for a 4 night stay, you'll appreciate the convenience of the GC.
I disagree with the comments about DLH's cleanliness. It's really nice. The rooms are actually bigger too and the in-room theming is nicer. Plus, the building that has the concierge in it is the best located building -- closest of the three towers to the parks. If you like character meals, the best one at DL is in the DLH.
All in all, GC is better. How much better? Depends I guess on how you value 88 points. To me, that sounds like about $800 to $1000 in cash value. That's a lot of money to me, but that's pretty much in line with the cash reservation difference between DLH and GC for 8 nights (or 4x2) -- actually maybe a little better. Can't go wrong either way. If you're in the mood to slurge, go GC.