Answer
$BrO^-$ is the stronger base.
Work Step by Step
The weaker the acid, the stronger its conjugate base. Therefore, if we determine which conjugate acid is weaker, we will get the stronger base:
Conjugate acids: $HBrO$ and $HClO$;
When comparing the strength of an oxyacid, the electronegativity of the central atom is an important factor.
Since $Cl$ is more electronegative than $Br$, $HClO$ is the stronger acid, and $HBrO$ is the weaker, which makes $BrO^-$ the stronger base.
