I've been a fan of the deluxe resorts since we have small children and sometimes it's just too much to wait for a bus with a stroller (that must be folded) during high traffic times. Sounds like your parents may have similar mobility issues, which I think might tip in favor of a deluxe. (This is also why I've been so hesitant with WL and AKL)
Also, as PPs have said, a deluxe is not worth it if you're just showering and sleeping but very well may be worth it if some of your group is going to be spending time at the resort. We've also stayed at the Dolphin, and would seriously consider it if they had Magical Express. Love the Epcot resorts for the proximity to the world showcase. It was so easy to pop over for dinner or an evening stroll/snack that even though our DD1 can do more rides etc at MK, we the adults like the Epcot resorts more. They're more peaceful than the contemporary, for sure. That said, it's going to be super crowded over Xmas week anyway.
It's been a dream of mine to go to WDW over Christmas; we've always stayed at deluxes but always at a deep discount (25-30%) or renting points, and in less than high season. I think you'll have fun no matter where you go, but given that you're 4 adults I might try to get a deluxe hotel room with 2 queens rather than a studio with a queen plus sofa bed.