Stainless vs. copper tubing is going to have virtually no effect on time to cool. The metal is not cooling the wort, it is the water running through the coils that cools the metal that cools the wort. While copper does have a much better heat transfer coefficient, even with needing to be a little thicker than stainless tubing for strength, in this application the temperate difference between the two metals with the water cooling is going to be very small and copper is only going to be seconds, if not less in cooling time. The true key to how fast you will cool using a wort cooler is the water temperature from your tap and how fast the water flows through the wort cooler moving heat away. The difference in these two metal materials is only going to have a minor effect. It like driving down the street 2 mph faster you will only save a few seconds.
The advantage of the stainless steel is that it is easier to clean prior to use and will not react with the wort. I have no idea if the minor reaction of the copper in the wort causes any negative consequence, it very well may not.
Now for those who think cooling small batches, 5 gal or less, in a stainless steel pot with a wort cooler is a lot faster than using an ice bath, this is just not the case. First the math will show the part of a 20 Qt. pot submerged in a 12” ice bath will have approximately a 40% larger cooling surface area than the coils of a 50' 1/2" wort cooler. You don’t get the same effectiveness as a wort cooler since you don’t have constant moving water that keeps moving heat away from the metal. So you have to take advantage of the larger surface area, slow self-agitation, and cooler ice water to make up some of the difference. You also have to have good control over doing water exchanges. What I have found works well for me is to start with an ice bath. Then after the ice melts I drain and refill using reusable ice blocks instead of ice. I consistently can cool in 20 minutes or less. I also have a stainless steel sink which helps dissipate heat but the sink also helps when using a wort cooler for pots that fit. For me the quicker set up time to use the sink only, lower risk of contamination, and less cleanup needed makes it worth the extra effort in controlling the ice bath and taking a couple extra minutes to cool. Anyway my 2 cents.
The advantage of the stainless steel is that it is easier to clean prior to use and will not react with the wort. I have no idea if the minor reaction of the copper in the wort causes any negative consequence, it very well may not.
Now for those who think cooling small batches, 5 gal or less, in a stainless steel pot with a wort cooler is a lot faster than using an ice bath, this is just not the case. First the math will show the part of a 20 Qt. pot submerged in a 12” ice bath will have approximately a 40% larger cooling surface area than the coils of a 50' 1/2" wort cooler. You don’t get the same effectiveness as a wort cooler since you don’t have constant moving water that keeps moving heat away from the metal. So you have to take advantage of the larger surface area, slow self-agitation, and cooler ice water to make up some of the difference. You also have to have good control over doing water exchanges. What I have found works well for me is to start with an ice bath. Then after the ice melts I drain and refill using reusable ice blocks instead of ice. I consistently can cool in 20 minutes or less. I also have a stainless steel sink which helps dissipate heat but the sink also helps when using a wort cooler for pots that fit. For me the quicker set up time to use the sink only, lower risk of contamination, and less cleanup needed makes it worth the extra effort in controlling the ice bath and taking a couple extra minutes to cool. Anyway my 2 cents.