Tony asked:

... some tadpole trikes... are available in a "big wheel"
version with a larger rear wheel... wonder what was the
reasoning behind that, what the advantages are presumed
to be. Smoother ride? Higher gear range?

IMHO, Tony's guesses are the right ones, in reverse order.
On the downside I'd list longer, taller and heavier trike,
and a bit more flex from the side loading wheels have to
deal with on a tadpole. As DD said:

... you don't have to gear up to compensate for that smaller
rear wheel. This means less need for Schlumpf drives, 3x7
[now DualDrive] internal rear hubs and other friction-causing
drivechain devices, or for dinnerplate chainrings.

With a typical narrow 406 tire (aka BMX or 20X1.3) the drive
wheel on a tadpole has a rolling diameter of about 19". With
an 11T small gear on your rear cogset, you would need a 58T
chainwheel to get a top gear of even 100 inches. That pretty
much means most contemporary tadpoles use road triple cranks,
and also exceed manufacturer's specs for both chainwheel
size and chain take-up.

With a 559 drive wheel (aka MTB or 26X1.5), you can use a
lower cost MTB crankset with 22-34-46 rings and an 11-34
cogset for a gear range of 17 to 107 inches. A 406 with the
same 11-34 cogset and a wider 26T difference at the crank
(32-44-58) has a range of only 18 to 100 inches - both a
narrower range and lower overall than the big wheel.

All else being roughly equal a big-wheeled trike will be
about 4 to 6 inches longer, and 2 to 3 inches taller than
a tadpole with the more common 406 drive wheel.

Regards,
Wayne Leggett
LoGo Trikes USA
Oxnard CA