Four coiling can make a trap react faster and can be a factor if you have added extra weight to the trap jaws, as in laminating them. As for "provides a lot more holding power", it does not. The lever configuration and the angle at which it meets the closing jaw has
significantly greater impact on the holding power of a trap as does four-coiling it.
I just got done "fixing" a number of Bridger #5 coils that were giving me problems in not holding beaver. The springs had grown weaker on the trap, and that indeed was part of the problem. But I fixed that problem not by replacing the springs, or adding stronger springs, I fixed it by changing the jaw configuration. I'll try to make a post on this.
I use a few four-coiled traps, but I don't find four-coiling at all necessary to make a standard traps function adequately. If they didn't work with two coils, manufacturers wouldn't be able to sell them that way.
-- Hal