Hi Jeff, I'm no expert, but from my research the reason the tri-radials have a longer life, which is perhaps slightly different from "lasting longer" has to do with the orientation of the cloth fibers in relation to the stretching loads. So by lasting longer what I understand is, they hold their aerodynamic shape longer, and maintain windward efficiency longer. Not to be confused with wearing out from chafe, uv, etc, which is a different concern. The tri-radial and crosscut seem to be similar in terms of wearing out, it's even possible the crosscut has a little advantage, so for the Joshua Slocum types, it's possible crosscut would make more sense. Also might be more durable if primarily downwind trade wind sailing, but I'm not sure about that.
The nature of non radial sail cloth is that there are fibers woven in perpendicular directions, and the way cross cut sails are made, the strains end up trying to stretch the fabric in directions which are not aligned with the orientation of the cloth fibers. By weaving crosscut fiber very tightly from synthetic fiber (as opposed to the ancient and short lived cotton) and then coating the cloth with some sort of resin, it is possible to stabilize the cross cut fabric from permanent stretch for a while, but not for too many years. A lot of it seems to come down to the durability of the that coating which is trying to lock the fabric grid in place.
In the case of tri-radial, the reason for the funny looking fabric pattern is to get the fabric's strongest and least stretch prone orientation in line with the strains on the sail. And since the fabric will be primarily strained in only one direction on the sail, they use special fabric for the purpose which puts more of the fabric in direct alignment with the stress, rather than trying to make it balanced for diagonal loading as in the case of cross cut sails. So the sail is less stretch prone because of the design layout, and the type of cloth that's possible to use when cut that way. A double win. It seems to be a fairly recent development to have specialized fabric for tri-radials. I believe in the first draft versions, they just oriented normal sail cloth so that the more stretch resistant of the two orientations aligned with the loads. As the sail became more popular the fabric folks seem to have said if that's what you are doing, we can make it even better. One downside on the cost front vs crosscut, a bit more labor to sew it all up, and bit more waste because of all the funny shaped pieces. I suspect modern software is pretty good at minimizing that waste though, by puzzling the pieces that can be used into a well nested template. I also suspect that modern software make the whole process of figuring out a proper 3d sail shape much easier compared to what must have been a seat of the pants affair way back when, even for crosscut sails.
Bottom line seems to be that airfoil shape is more durable in a tri-radial due to the design of the sail, and the special cloth they are able to use. For me it will be new territory to have a sail that's not decades old and really only efficient on a beam reach or downwind run. Since my E32-3 furling genoa is NOT original, and seems to work pretty well, I can really appreciate the windward potential of the boat, and I can see in the old main shape that it's not contributing much to that forward progress if I sheet it in to where it seems like it should be. The draft looks too far aft, and the back half of the sail seems to be countering any pull in the forward half, and most likely creating plenty of drag too. Not to mention the tell tales are telling tales of air flow chaos up there! I can never seem to get them all going in the same direction going to windward. Might be part of my learning curve, but I would expect a sweet spot in there somewhere and it's been elusive.