Answer
$BrO^-$ is stronger than $Br{O_2}^-$.
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 $HBrO_2$;
When comparing the strength of an oxyacid, the number of oxygens is an important factor.
Since $HBrO_2$ has more oxygens than $HBrO$, $HBrO_2$ is the stronger acid, and $HBrO$ is the weaker, which makes $BrO^-$ the stronger base.
