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"Three-layer" is polyethylene, not vinyl. They say it's better than regular polyethylene, but it's still heavy, and it still gets deformed over time.
Polyethylene works well for the new, very tiny solo whitewater canoes, which are very similar to kayaks (kind of tubular and therefore self-reinforcing), but I personally don't like its inability to maintain shape in conventional canoes (which are not tubular, and thus prone to flexing and deformation). I have yet to see a polyethylene canoe (other than brand-new boats in the showroom) that doesn't have all sorts of terrible warping on the bottom.
Polyethylene is cheap though, and very tough.
some people prefer wood canvas over royalex and kevlar etc. Probably not the conventional view. But there is merit to it. Read Becky Mason's discussion on her web site. She is a devote of WC even for the flat water freestyle stuff she does.
I had one kevlar boat in my life. It sure was nicer to carry on land and I liked that. But on the water? Ugh. Too light. It sat on top of the water instead of in the water. It got blown around something awful. I am slowly coming around around to the point of view that our modern canoes are just too darn light and it has a negative impact on the paddling performance.
As between Royalex and 3 layer, I vote very strongly in favor of Royalex. For the reasons all ready stated.