I have not found the no stink claim for wool to be true for me. Maybe my body chemistry is weird or something, but my wool garments stunk the worst of anything I had along when I tried any wool for touring. Synthetic vary as far as how much/if they stink. I choose ones that tend not to to take along on tour. Synthetics hold less water to start with and dry faster. I find them a little more comfortable, but both wool and synthetics come in a variety of textures so feel can vary quite a bit.
Way back in the day I used to wear wool becase that was all there was for wet use that worked at all. Yes I am that old. I have to say that I was so happy that I was willing to live with the early synthetics for my whitewater canoeing, kayaking, and other wet outdoor activities despite the fact that the early stuff was VERY stinky. Now that the newer synthetics are not bad in that regard I am not hesitant at all to choose synthetic garments.