Wet synthetic often feels cold and slippery. Yes, I said cork can be slippery when wet too, but if it's a matter of contamination, you can fix it with a little steel wool. To be fair, this is one of my biggest biases against man made materials, and was formed for the most part, when I was younger and materials of a lesser quality were available than what is today. According to information that I've read recently, these problems are supposed to be a thing of the past. Since the surface is porous, it can stain.
Foam transmits less vibration through to the angler than a harder material.
Since the whole idea is to build the best rod that you can, I consider it self-defeating to intentionally use a material that I know has inferior vibration transmission qualities. Some solvents may affect the material by softening it or dissolving it completely. This really should be a moot point. Now that you have a basic understanding of the differences between the two materials, you need to decide how you want to build your handle. On the other hand, you can order handle components that are glued and shaped before you get them so that the only thing you need to do is fit it to the blank and glue.