First off, you're going to want to figure out the immersion chiller's flow rate. Depending on your water pressure, tube length, and tube diameter, I think it could range anywhere from 1 gallon a minute to 10 gallons a minute.
You can approximate it's output by timing how long it takes you to fill your carboy with a garden hose or sink, whichever applies to your chiller. Your gallons per minute = the size of your carboy (in gallons) divided by the elapsed time to fill it (in seconds), multiplied by 60, so:
(CarboySize/FillTime)*60 = GallonsPerMinute
Once you have this, you'll have to scale down to compensate for the area difference between the hose and the tubing. Remember area=Pi*radius^2? I always wondered when I'd put it to use :-)
Lets say you have a 5/8 inch hose, so the area would be:
Pi * (.625 / 2)^2 = ~.3068
Lets say you have a 3/8 inch, 25 ft chiller (this seems to be a popular one), so the area would be:
Pi * (.375 / 2)^2 = ~.1104
So I would guess it would have about a third of the throughput:
NewGallonsPerMinute = GallonsPerMinute / 3
So assuming your hose and chiller are the sizes indicated above and your hose can put out about 10 gallons per minute, your looking at about 3 gallons per minute for your chiller.
Your cool-down time will depend on whether you just sit the chiller in the pot or you agitate your wort a lot, as well as your cold water temperature and your copper coil surface area. But if you go by previous posts on this site it sounds like times of 20 minutes seem to be average, costing you about 60 gallons of water.
If you really want to you could apply Newton's law of cooling to calculate how fast it will cool. Basically the more surface area (the longer and wider your tubing), higher temperature difference, and faster water flow you have, the faster your wort will cool.
Note that temperature difference is only the temperature of the water and wort touching the tube walls, not the other wort sitting around, so a great deal depends on liquid turbulence. This isn't a big deal inside the tube, since the flowing water is very turbulent, but if you just sit your chiller in your wort and don't disturb it, you'll notice cold water coming out of your chiller while your wort remains hot.
As for which ones use less water than others, doubling your tube length doubles your surface area, but actually only gives you about a 50% increase in efficiency. That's because the surface area you gain by lengthening the tube doesn't have an affect at the beginning, but gradually increases efficiency as you chill. The temperature difference at the beginning is just too great for it to matter. Doubling the tube width, actually gives you better efficiency than lengthening, but that's do to the fact that you're increasing the flow rate as well as the surface area.
So if by efficiency you are referring to the speed you can chill, the more length and diameter, the better.
If you're wanting to save as much water as possible while also cooling quickly, go for a chiller with more length.
I've also seen chillers that have the coils all bound or soldered together. This won't be as efficient as an unbound chiller of the same length due to the decreased surface area.