Some nylon shirts are clammy feeling because they are so tightly woven and don’t wick well, but not all are like that. Nylon is starting to be made more wicking either by coatings or altering the fiber shape (from round to something like what a coolmax fiber looks like, which is sort of like a more rounded version of this–X).
There are some nylon shirts that have just enough air porosity (“breathability”), but are tightly woven enough to still protect. For example, an older style Kuhl Wunderer shirt that I have. The Kuhl shirt is also wicking, so between all factors, it is not clammy. An inexpensive nylon shirt from Bass Pro shop that I bought which is quite tightly woven and non well wicking is definitely clammy feeling.
Same with polyester. It depends on how tightly woven and whether or not it wicks well as to clamminess. Polyester and nylon have a similar surface energy, though nylon is more moisture absorptive in the actual material itself. Point being, both can be made to be either well wicking, or very bad at wicking, or breathable or not. If you just have round, extruded fibers (and without a coating) then neither nylon nor polyester will wick well at all. Alter the fiber shapes, do bi component fabrics where one layer has thicker and one has thinner fibers, or add a coating (least preferable since it’s not permanent), to induce capillary action and both can be made to be highly wicking.
I prefer nylon over polyester for warmer weather because it’s less stinky, stronger for it’s weight, is less dense, and if all other variables are the same, feels slightly cooler on the skin than polyester. I like polyester-wool blends for colder weather, but these are usually knit. Not sure I’ve ever seen a tightly woven polyester wool blend shirt or even fabric by the yard before. Polyester wool blend pants are also nice for cool and colder temps, and often can be found quite cheaply at thrift stores. And you get to hike in style… (they’re usually dress pants). That’s meant to be a bit ironic, because I could care less how I look on the trail except for garish colors.