I just received the parts yesterday to add a re-circulation port on my BK, so I can do a proper whirlpool as well as have more control of my wort temperature after flame out. I use a plate chiller and plan to run the whirlpool through it to get the temp quickly to 180F (then shut the water off to the chiller), late addition hops for TBD time and then to fermentor. I also have a hop rocket between the BK and plate chiller that I use rice hulls to prefilter before the plate chiller (works really well). Of course I recirculate the really hot wort first to sanitize it all before going to the fermentor.
I started using the prefilter because a plate chiller is a PITA to clean if trub or hops get in it. And I use a plate chiller because it uses the least amount of water to chill. I have well water that is 62F year round (deep well) so it only takes me 5 min to go from BK to fermentor. The plate chiller is only 20 plates, but it is 18 inches long, which is the biggest contributor to the 5 min chill time. (It's the length that mainly controls chill eff. and the number of plates mainly control the pressure drop between the input and output of the chiller. The number of plates does add a little to eff., but not like length. If you are using a pump, then for a homebrewer pressure drop is not an issue. If you use gravity, then more plates will move more wort. Always a trade off somewhere.
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If being green is not quite so important then the counter flow chiller is probably the next best thing, and better than an undersized plate chiller. The least expensive, and probably the easiest to maintain and in my opinion uses a lot of water is the immersion chiller, and works best if you have some way to whirlpool at the same time.
All that said:
1. the plate chiller gives me more control of temp and time after flame out for hop additions and I can keep the lid on the BK to minimize hop aroma loss. I plan to experiment with different post boil temps with hops, so I need the better control temp so the brew day does not get too long.
2. the immersion chiller of the dunk variety will require the lid to be off more than on probably (i've not used one so someone who has should jump in), and getting to 180F or below will take longer, but still as effective for post boil hopping.
3. It's back to what you feel comfortable with and what you prefer as a brewing process as well as time vs expense.