Which accommodation?

Parks, resorts, dining, attractions, vacations

Flight from London Gatwick to Orlando, direct with British Airways,
and four nights at Gaylord Palms (Florida view room) is same price as
flight and four nights at Caribbean Resort ("Standard" view).

Deal for one flight ticket and the hotel (I assume double occupancy
will not be a problem) is $1,700.

Bit steep for four nights, but there's an element of "compassionate"
travel here (cancer patient).

Any arguments as to which is the best deal...or suggestions for
equally pleasant trips?

Flights on January 3rd and 8th are pencilled on the calendar.

I've only looked on Orbitz, so far. Can't confirm until dates are set.
Gaylord Palms, though I've never stayed there, looks very nice and
it's a short drive to WDW.  However, if you are only doing Disney I
would really recommend staying onsite for the total immersion
experience.  You will save in transportation costs too.  If you can
swing a moderate resort, that would be my recommendation too.  Rooms
are a bit larger and amenities a bit better than value resorts.
Caribbean Beach (the OP's other option besides Gaylord Palms) *is* a 
moderate resort, isn't it?