I've used both plate and copper-tubing-inside-a-garden-hose chillers, and without a doubt, the copper CFC is the way to go. Cleaning a plate chiller is a very tedious process. Flush and then backflush and then flush and then backflush and you STILL get bits of hops and junk coming out. I don't think I ever really got my plate chiller perfectly clean.
Dealing with a clogged plate chiller makes you want to throw things (like a plate chiller) across your yard. My copper pipe CFC has never clogged on me and I don't usually filter my wort on the hot side.
This is my routine for my CFC:
About 5 minutes before flameout:
1) Drag out the CFC
2) Hook up the water hose to the female garden hose QD on the chiller
3) Hook up a waste water hose to the male garden hose QD on the chiller (I use different QDs to ensure that I'll never accidentally hook the wrong hose up to the wrong end)
4) Turn on the valve on the water inlet to verify everything is good to go and then shut the water off again
5) Throw the tubing for draining from chiller to carboys into a bucket of Star San
At flameout:
1) Hook up tubing from BK to the pump inlet
2) Hook up the tubing from the pump outlet to the chiller wort inlet
3) Hook up tubing from chiller wort outlet to carboy, but put the other end in your vorlauf pitcher instead of the carboy
4) Open up the BK valve and make sure that the pump is flooded with wort and turn on the pump
5) Watch the other end of the tubing for old water that was sitting in the chiller from the last brewday to start flowing out
6) Once all of the old water is out and hot wort is flowing, put the end of the tubing into the top of your BK and recirculate the boiling hot wort through your chiller for a minute or two to sterilize the chiller insides
7) Turn the cold water on to start chilling the wort
8) Use a Star San spray bottle to spritz the outside of the carboy hose and your hand one more time
8) Start pumping wort into the carboy(s).
Cleaning the chiller:
1) Run water through it for a minute
2) Try to drain as much water out of it as you can. You'll never get all of it. It somehow magically produces more water whenever you move it around. They should sell them to desert communities as a never-ending source of water.
3) Put it away
Obviously, some people would lose sleep thinking about all of the horrible things that are growing inside their CFCs, but a) copper is a naturally anti-bacterial material and b) sterilizing the insides before each use really goes a long way towards nice bacteria-free wort and c) if you're the type of person that would worry about such a thing, then maybe this whole CFC thing is just not for you.