During audio post-production, after all panning, mixing, and track EQ is finished, we often do a mastering pass that involves another EQ and compression to the mixdown for a fuller result for the film. We often ask ourselves this question: EQ or compression first?
Michael from In The Mix tells you his preferred filter sequence in this video on YouTube. While this was meant to be a music production tutorial, his tips applies to audio production in videos too. Most importantly, he tells you the reasons as to why he does it his way. The comment section is rather helpful as well.