As far as the shipyard tells it changes only the distance at which you can engage the interdictor. Which in turns makes it easier to interdict in most cases since the closer you are to a target (relative to the maximum possible distance), the easier the interdiction is. I think that relative speed also plays a role in how easy it is.
But concerning our Fed friend, I interdicted him multiple times with a 4C interdictor yesterday, sometimes very close (less than 30 ls) and while going much faster than him. Yet and even though I managed to keep him dead-centered in the reticle the whole time and he was not moving a lot, I couldn't pull him out of supercruise a single time except if he submitted.
I wouldn't say that I'm the best pilot out there or that I know game hidden rules in-and-out but I've interdicted my fare share of player pirates before, and none had escaped every time with so little apparent effort and me being totally unable to get my interdiction gauge up even by a tiny bit ...
This is pretty suspicious if you ask me.