Should we use EQ before compression or after?

Both.

I remember coming across what someone described as the “Triple-C approach” to processing audio (I wish I could remember the source)– Correction, Compression, Colour.

This obviously applies to many other effects, but in terms of specifically answering the EQ/Compression order:

  1. Correction: EQ to remove unnecessary and annoying frequencies
  2. Compression: to control dynamics and envelope
  3. Colour: EQ to add colour, adding body, presence, air
mixing