I know for a fact that A6-EBA is a Boeing B777-31H/ER so I don't know why it's being assigned B773.
However, the difference between a B773 & a B77W is the range and the M.T.O.W. (B77W) having higher specs...
May I ask where you saw A6-EBA marked as a B773?
Cheers,
EK433B77W! ^