BrO₂⁻;

It is less stable due to poorer accommodation of negative charge by lesser O atoms and its oxyacid HBrO₂ is a weaker acid due to a lesser degree of electron density withdrawal from the O-H bond, making the bond stronger and less susceptible to deprotonation.

BrO₃⁻;

It is less stable due to poorer accommodation of negative charge by more O atoms and its oxyacid HBrO₃ is a weaker acid due to a lesser degree of electron density withdrawal from the O-H bond, making the bond stronger and less susceptible to deprotonation.

Neither of the two;

The two conjugate bases of oxyacids are similar in strength since the central atom is the same.