Both work ....with decidedly different results.Which is best for the task at hand can only be answered by the pair of ears hearing the source at hand.

One "rule of thumb" to keep in mind -

If you're correcting the sound with EQ - reducing rumble, hiss, siblance, honky midrange, etc., you'll probably want to EQ it first. This way, the compressor won't be making the problem worse or reacting to things that won't be there later.

An extreme example would be a plosive in a vocal track - If compressed first, the plosive would duck the vocal down fairly drastically depending on the settings. If you EQ the plosive out before the compressor, the compressor won't react to it anymore. If the plosive is EQ'd out later, you're "cleaned up" vocal will suddenly duck down for no apparent reason.

If you're enhancing or shaping sound, you might want to compress first so the compressor isn't fighting with the EQ.

Again - "rule of thumb" - Not "rule."

thanks guys, I've been saved again by recording.org!
Chris Paulson
http://www.chrispaulson.de