Sometimes your machine will decide for you! For example, my Juki TL2010Q definitely does not like the polyester invisible thread, but I'm able to FMQ with the nylon invisible. Today's nylon invisible is much softer and finer than it was say 10 years ago. I've had great success with Essence nylon invisible thread, that I order from 3 Dogs Quilting in Ottawa.
My other machines, a Juki DX7 and an old Singer, will handle both polyester and nylon successfully.