Answer
$0.0100M$ $KClO_2$ is more basic.
Work Step by Step
1. Identify each conjugate pair of the ions in the solutions.
First solution:
$K^+$: $KOH$: Strong base.
$Cl^-$: $HCl$: Strong acid.
Second solution:
$K^+$: $KOH$: Strong base.
$Cl{O_2}^-$: $HClO_2$: Weak acid.
2. Therefore:
First solution: Neutral
Second solution: Basic.
So, the second solution is more basic.