Acid strengths for HBrO4 vs HIO4, and HBr vs HI

So I was looking at factors that control the relative strengths of acids and bases.

We know that $\ce{HI}$ is a stronger acid that $\ce{HBr}$ because $\ce{I}$ is a much larger atom.

But then, I read somewhere that $\ce{HBrO4}$ is stronger than $\ce{HIO4}$, because in this case it's electronegativity that plays the important role.

How do you know whether to use size or EN as a guideline for comparing strengths of acids/bases?

• In HI and HBr, the hydrogen is directly bonded to the halogen, but in the perhalic acids it isn't. – f'' Aug 14 '16 at 16:25

$\ce{HBrO4}$ and $\ce{HIO4}$