I am going to disagree with most who have responded. I've stayed in both hotels more times than I can count. I vastly prefer GCH currently. I stayed at DLH in July, Oct, and one night in Dec. I stayed in GCH in Dec and Jan.
DLH has lost most of what I used to love--the restaurants, shops over the water, waterfalls, and many other things that were unique to it. It feels run down and old to me. I love all of the memorabilia but I think it's regrettable that there is no unifying lobby area, just a place for your family to sit while you're checking in. You used to see characters roaming through and there were fun activities. The monorail slide is neat looking and the pool is nice but it closes early and isn't enough to sway me anyway since I'm not going to hang out at the pool (I have one at home). The only dining they have right now is Goofy's, which I think is buffet, Trader Sam's (which I love but has very limited capacity) and Tangaroa, which is more or less fast food. There's a tiny take-out coffee place also which gets slammed in the mornings. There are encouraging signs that Steakhouse 55 may be returning, though! But with the addition of all of the new DVC rooms, it's going to be even more difficult to get food at the hotel.
A lot of the rooms are slightly larger than those at GCH. The huge windows are nice, but the construction is going to greatly impact many of the views. It may not seem much farther than GCH, but it feels a lot farther when you're walking back at night. The elevators were super slow when we were there last month. We had a premium concierge room one floor below the lounge, and it often took forever for the elevator to come. We'd stayed the first 3 nights at GCH (std) and the 4th night at DLH. The premium concierge room at DLH felt like a big downgrade, though we did have a beautiful view and could see the fireworks. Concierge food was terrible. It used to be wonderful but now its tasteless and definitely not worth it for us so I can't recommend concierge.
Lots of people love the headboards that light up and play a little song. If you've not seen it before, or if you have kids, it will probably be cool. I don't even look at it any more and it feels cheesy to me now. I prefer the bathroom setup at GCH, where someone can be in the shower/toilet room and others can get ready at the separate vanity area. The showers at GCH are huge and pretty cool.
GCH currently has a better dining selection IMO. They have multiple areas including a kind of short-order/cafeteria-style set-up, lounge, poolside bar and grill, fine dining (Napa Rose), and buffet (Storytellers). The lobby is wonderful, though at peak times of the year it can be crowded. I've never had trouble finding a place to sit and I love hanging out in the big rockers by the fireplace. There is also an outdoor fireplace directly behind the indoor one.
I know that money is probably the main factor in most people's decision about which is better, and DLH is nearly always better price-wise. But there are some good offers throughout the year and cheaper times to go. That can really affect the room cost. For example, we paid $800+ per night for a std room at GCH in Dec. with a MK rate. We paid $389/night for the same room earlier this week, also a MK rate.
I'm not trying to bash DLH, as I do love it and it's where we go when younger kids are with us. When it's adults or adults and teens, GCH is the favorite in my family. Both hotels are great, but my preference by far is GCH. I almost always reserve a std room and request one close to the elevators. I don't care about the view because they're almost all pretty good and none are worth extra to me.
Good luck with your decision and honestly, your attitude is the most important thing! Have fun!