Polypropylene grograin or webbing is normally better then nylon because it absorbs less water, hence dries faster, hence reduces the chance of mildew. For the same reason, guy lines should be polyester. The only reason I can think of using nylon grosgrain or webbing is because you plan to abuse the pullouts, such as by pounding stakes into the ground with a rock while the stakes are inserted in the pullouts--there is a good chance the rock will hit the pullout fabric and cut it and nylon is much more durable than polypropylene. But this is a bone-headed move to begin with, since there is also the possibility of slipping and cutting the silnylon.
To give some idea of the importance of fast-drying pull-out loops, this is the only part of one of my old Outdoor Research bivy sacks that ever mildewed. The Goretex top and coated nylon bottom dried fairly quickly, but the pullouts seemed to take forever to dry. On cloudy days, I just gave up waiting and the result was mildew.
As for the all this hoopla about catenary curves, I hope everyone is aware that all nylons stretch, especially when wet (such as from condensation or rain) and thus a catenary curve is of limited importance with tarps. Far more important, in my experience, is strong reinforcing at the pull-outs, so you can really tighten things up, especially on the ridgeline. In my opinion, merely stitching a reinforcement patch is insufficient. Far better is to glue a reinforcement patch to the tarp using Silnet seam-sealer. Not only does the glue itself reinforce the tarp, but the glue evenly distributes the forces across the entire area covered by the reinforcement patch, whereas stitching distributes the forces to only the line of stitching. I once ripped out the ridge-seam pullout of an Integral Designs SilShelter while trying to tauten things up.
In any case, mathematical catenary curves are misleading. What you are really trying to do is compensate for fabric stretch, which is different with the grain, against the grain, and diagonal to the grain. This has nothing to do with mathematical catenary formulas, however it turns out that the mathematical catenary formula gives a decent enough approximation in practice. Technically, the correct approach is to pull on the tarp fabric at the points where you would be putting the pullouts and then see how the fabric stretches and wrinkles, and then cut out some of the wrinkled area. Because of the margin for error associated with cutting fabric, especially by hand, any smooth curve is going to work--catenary, parabolic, whatever--as long as you don't cut too much off.