Hi pebbles, there's lot's of people who know more about this than me but I'll tell you what I know.
Rayon does break a bit easier than poly. You can't bleach rayon but you can bleach poly Historically rayon had a much better sheen than poly but with the tech advances made the gap has been reduced if not eliminated.
I use them interchangably but I do have more rayon than poly. Mostly because melcomart had a big sale ($1.25/1000m) on rayon when I set up my thread stash. They are currently selling it for $1.91 rayon $2.25 poly. I do have other kinds of thread - marathon canada and some variegated I got off the web from Minrak. I'm happy with all my thread. I've heard of people having lots of breakage problems but I've never experienced that. I have found that the customer service from all 3 places has been exceptional.
However, I find the type of spool matters to me. The Melco and Marathon (and I'm sure lots of other) spools are a cone with a splayed out end. You can set them up on end. Some maufacturers have spools that are just a tube with the thread wound on them. I have found the tube thread sometimes likes to unravel (the thread slips off the edge) making a mess - I have to keep full threadnets on them at all times. You don't have this problem on the splayed cones
I haven't experienced shrinkages problems with any of my thread.
Good luck and happy embroidering
homebody