Answer
$S^{2-}$ is larger than $O^{2-}$ since $S$ is below $O$ in the periodic table and ionic radii increase as we move from top to bottom across a column.
Work Step by Step
Across a column in the periodic table, for ions having the same charge, ionic radii increase as we move from top to bottom, due to the increasing values of $n$, meaning there are more and more orbitals available for electron occupying that are further and further from the nucleus.
In the periodic table, $S$ is below $O$ and they are in the same column. That means $S^{2-}$ is larger than $O^{2-}$ according to the above trend.
