There's only one An-225, and I do believe it's Antonov that operates it.
I tend to agree that maximum takeoff weight is the best measure of 'size' for an aircraft. Otherwise, as pointed out, you have to pick which other dimension to choose. Length? Wingspan? Height?
I believe the Spruce Goose is only the biggest in terms of wingspan. Personally, I don't consider that to be nearly as 'important' an indicator of size as weight, or, even better in my opinion, payload/internal volume. An-225 measure on all such measures, as well as in thrust, I'd imagine. I think people only call the Spruce Goose the world's largest plane, basing the calculation on wingspan, because they want it to remain a tourist attraction. However, I guess at the time of its construction, it was probably also the heaviest/longest plane, etc. Not that it ever flew anywhere!
when the A380 arrives, I guess it's dimensions wil be very close to the An-225. Not much bigger, if at all.
Next flight.... who knows.