I’ve been following this conversation for a while and thought I’d chime in. I use both personally. I use an Immersion chiller coupled with a pump for recirculating/whirlpooling for heavily hopped beers (link for reference photos), and a CFC for everything else. I only do 5 gallon batches (for now 
). The immersion chiller with the recirc setup can drop from boil to 170 in 5 mins or less easily, then once my whirlpool is finished, it takes probably 15-20 mins to get down to the upper 60s. I got my immersion chiller free as part of a sale our hosts were running a few years back, a bigger one would help with time on this.
For 90+% of my beers, I use my CFC. I have a gravity fed setup using my Little Giant Ladder with two platforms.
It’s probably not ideal to lift 6 gallons of boiling liquid to the top platform and eventually I’m hoping to get an electric side by side setup, but that’s down the road a ways. Ground water temp varies by season so in the winter, I actually have to turn down the hose volume to keep it from chilling too cold, because it will easily get down into the 50’s in the dead of winter. In the summer I typically run full bore with the hose and the valve on my kettle about halfway open and get it down to the upper 70’s as fast as I can run it through the chiller in my gravity setup, then the carboy goes in my swamp cooler setup with ice bottles, until it’s down to pitching temp before bed.
As for cleaning, I simply run StarSan through the CFC from a bucket and cap both ends with StarSan in it. I’ve never done anything more than that and never had an issue in over 4 years. Occasionally it will get clogged if it’s a highly hopped beer, but then I simply use a bike pump to force air through it and that always solves the issue.
The immersion chiller setup, I spray and scrub off the outside of the chiller and the inside of the kettle, then refill the kettle, heat to 120, then add PBW and recirc everything for about 20 mins. Then I dump that, rinse down, refill to cover the chiller, reheat to 100ish, and recirc the rinse water through everything for about 10 mins. The chiller/pump recirc setup takes about an extra hour total to clean up, but most of that time I’m off doing something else and only go back when the timer goes off.
Rad
