I have tried ice bath, immersion and plate chiller.
The plate chiller is by far the quickest, It takes me around 30 mins to get down to pitch temperature with the IC, whilst the PC it takes about 5 mins or less and that's to 61F, I couldn't get much colder than 67F with the IC even after 30 mins. This using using mains water, you can set up a gravity or pressurized cold liqueur tank for even faster cooling, this would able you to open the pump speed more and drain the brew kettle faster, I suspect it would just take a few minutes this way. The cold break I get on my plate chiller is really noticeable compared to the immersion chiller too.
Cleaning is more difficult than the IC, especially if you don't have a pump. If you do have a pump like me you can recirculate hot PBW solution through the chiller and then reverse flush. Then rinse by filling the grant continuously with water whilst having the return hose to the drain. I always chuck in some left over starSan before a final rinse just to act as an acid rinse not make sure there is no PWB residue. Its not hard, just time consuming and needs to be done straight away.
If you don't have a pump you can using a piece of tubing with a hose connection at one end and a brewery fitting (eg camlock) at the other and simply flush the PC from the mains water supply. Of course you can't use PBW in this way but you can gravity feed it from the grant.
To santize is easy, I connect the pump and PC to the brew kettle whist bringing the wort to boil, I then circulate for ten minutes at boiling. Again if you don't have pump you'll need to put it in the oven for a hour.
So basically PC performs significantly better, however they are significantly more expensive, especially once you add the price for the pump, hosing, connections and grant and they are more time consuming to clean and sanitize. That said a brewery pump can be used for a multitude of applications, recirculating wort, filling the brewkettle, vortexing for a whirlpool.
The other thing you'll need if you go with a PC is a hop filter of some kind to stop the PC getting clogged. I use a 400mirco hop spider. Works fine. My PC can take up to 900 Micro particles.
So the choice of PC vs IC is largely a budget question but also a question regarding overall brewery design such as if you want to have a pump for your mash tun. Space is also a consideration especially verse a counterflow chiller. PC use up very little space.
Also not all PC and IC are made equal, you need to consider the the Kw rating of the PC verse the length/diameter of the IC. My IC is relatively sort whilst my PC is rated to 125Kw.