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?
"We know that HI is a stronger acid that HBr because I is a much larger atom"
That is only half the story. It is about the strength of the H-Br versus H-I bond. Since I is larger than Br, the H-I bond is longer, weaker, and therefore more prone to dissociation. See here for more in-depth discussion.
$\ce{HBrO4}$ and $\ce{HIO4}$
both have the acidic proton bound to oxygen:
The H-O bond is approximately of equal strength in both acids and therefore you turn to electronegativity arguments.
