Plate counterflow chillers definitely could use a filtering system, and you'd need to filter before it hits the plate chiller or else there's a very good chance it's going to clog up on you, and that makes for a pretty miserable brew day.
Your copper/garden hose counterflow chiller doesn't really need a filtering system, but if you'd still like to use one, you could filter it before or after.
For filtering before, you could build a hop screen for your dip tube, made out of stainless steel mesh and sewed up with some stainless steel wire. I've made a couple of these, and they work well. Keep in mind that filtering before will not filter out the cold break, so the cold break trub will still make it into your fermentor.
For filtering after, you could buy something like Brewers Hardware's trub filter. People say that it works pretty good, but I'm not sure if it's designed to be used after a counterflow chiller instead of before the chiller. The cold break, combined with the hot break and the hop trub might clog it up too much. I don't know.
Another possibility is to use the copper/garden hose counterflow chiller and just let everything flow into the fermentor, wait an hour or so for things to settle, and then rack to another fermentor, leaving most of the trub behind. I did this for a kolsch just to see if it would make a difference in clarity and taste. Can't say it made much of a difference.
