I've used both. Here's what I can say...
The CFC gets the job done faster - period. It takes the wort from boiling to almost ground water temp in just a few seconds, and 5 gals only takes 15-20 mins. I noticed more cold break when I made the switch and I think the beers have been clearer without the chill haze problems I had before. All of the cold break goes into the fermenter, but I haven't seen any ill effects.
The CFC is definately more work to sanitize and maintain. I bought one that has vinyl tubing on the outside and it's really been a pain. The tubing has slipped off when it was cold and it constricted. One of the solder points has also broken that I had to fix.
The other thing is a CFC takes more attention to get the temp right in the fermenter. This assumes you're not recirculating the output back into the kettle. If you are, then most of the points I made are moot.
One of my next purchases will be a plate chiller. A shirron is only a little more than a cheap CFC and cheaper than some of the all copper CFCs like the Chillzilla. Plus, you can throw a plate chiller in the oven to sanitize - way easier than having to drain sanitizer through a CFC and then trying to drain it all out!