We just got back from DL and we stayed at the GC for the first time. (All other trip were at the DLH.) My DH and I both agree that we prefer the DLH.
Don't get me wrong, the GC is wonderful! The lobby and grounds are amazing!!! We had Theme Park view and it's really hard to describe just how cool it is to sit on your balcony and watch the monorail whiz by or the geysers going off on GRR! That said, we like the DLH better. The rooms are larger, the grounds more appealing (to us) and it is closer to DL via the monorail.
The GC is a very sprawling hotel and our walk to the elevator was LONG!!! (I had read a few complaints about this before we left and honestly thought they were exaggerating!!!) We were in rooms 3446 & 3448 if you want to look on the map. The elevator for our wing wasn't even in the main building!!
The plus to the GC was it's closeness to DCA. We found it was usually faster to go through DCA to get into DL, but I prefer taking the monorail from DLH.
The beds at the GC were wonderful!!
Amy&Dan is right, the GC does have balconies and I have never had a room with one at the DLH. But they have the slider and you can pull your chair up.
I have to agree with
klh999 the DLH just has a really good feeling!
We are making our first trip to WDW this fall, so I can't give you a comparison to the Poly. I have heard WDW people express disappointment with the DLH because they don't feel it's as "Themed" as the WDW resorts.
I think you and your DH will be happy with either and I bet the kids would prefer the DLH. (And think of the souvenirs you can get with the money you'll save!!)