I would say that to stay in either the DLH or PPH would be fine - I like them both - but make sure you spend time in the lobby/lounge area of the GCH. Santa and the carolers visit all 3 hotels, but there is something extra magical about the setting of the GCH during the holiday season that surpasses the other 2 hotels. Since the GCH already has that decor and vibe of a sort of elegant mountain lodge, it lends itself perfectly to the Christmas/winter feeling. Dark wood and dim lighting, along with the rustic but beautiful Christmas tree, enhance that atmosphere. I always say that the only thing that's missing from the GCH during the holidays is snow on the ground.
First of all, the GCH lobby area has very comfy chairs and sofas, which welcome people to come in after a long day and plunk down to people-watch or recap the day's events. It's sort of a communal and yet intimate area around the giant Christmas tree, and everyone kind of chats with each other while sipping beverages or munching on treats, or offers to take pictures of other groups by the tree. It's a very friendly feeling. In the evenings, a guitar player strums holiday songs by the fireplace in the hearth area. When he takes a break, the pianist plays familiar carols to keep everyone in the mood.
Then, Santa appears by the GCH tree every night (he does mornings and afternoons at the DLH and PPH), in intervals, with a PhotoPass photographer (the GCH is the only hotel of the 3 DLR hotels where Santa has a PhotoPass photographer with him). The carolers then arrive to perform their set in this most cozy setting, and children curl up on the floor to listen, while the adults - with drinks in hand - shout out Yuletide requests.