Immersion chillers use a lot of water. You can recirc ice water, but only after you drop it some and then you need a pump, too.
My biggest gripe about the immersion chiller is that it's in the kettle. I'd like to do a real whirlpool, not just a recirc of the wort to aid in cooling. The chiller interferes with the ability to separate trub (hot break and hops) from the wort. Not as important for ales, but lagers definitely benefit.
Without a CFC or plate, (supposedly - mind you, I haven't tried yet) you can whirlpool while hot (when it's most effective) let it settle and develop a cone, then pump through your chiller to drop to pitching temps. You won't separate cold break this way, but cold break is what has the good stuff for the yeast. Some lager brewers will try to remove some of that as well by floatation or other methods.
Debating a CFC or plate chiller,