Answer
$HClO_3$ is the stronger acid.
Work Step by Step
$HClO_3$ is one of the 7 common strong acids.
Since $HClO_3$ completely dissociates in water, and $HClO_2$ doesn't, $HClO_3$ is the stronger.
$K_a(HClO_3) > 1$
$K_a(HClO_2) \approx 1.1 \times 10^{-2}$
