Answer
$HBrO_3$ is stronger than $HBrO_2$ because, it has a greater number of oxygens connected to the central atom (Br).
Work Step by Step
For oxyacids with the same central atom, the difference will be the number of oxygens.
A higher number of oxygens causes a greater stability of the negative charge on the conjugate base, which increases the acidity of the compound.
Other reason: since $O$ is electronegative, it increases the polarity on the $O - H$ bond, increasing the acidity of the compound.
