I don’t have the exact quote but in high school English it was required reading that we read this sci-fi book called Unwind and one of the protagonists actually made this connection.

“There were two types of cops: the bullies who peaked in high school that want to keep reliving their glory days, and people who were bullied that want to oppress undesirables as a misguided way to get revenge on ‘wrongdoers’.” - Unwind (not exact quote just what I vaguely remember.)

But it explains the two types of fascists and those in fash jobs perfectly.

EDIT: Here’s the full quote -

“The way Risa sees it, there are two types of people who become Juvey-cops. Type one: bullies who want to spend their lives reliving their glory days of high school bullying. Type Two: the former victims of type ones, who see every Unwind as the kid who tormented them all those years ago. Type twos are endlessly shoveling vengeance into a pit that will never be full. Amazing that the bullies and victims can now work together to bring misery to others.“