As stated earlier not all poly battings are equal . Bearding comes from the fibers migrating through the fabric on the top and backing. So much has been done to prevent this in modern batting. Look for bonded fibers( they take the batting and run them through a high enough temp to literaly melt them together or bond them together) or a poly batting that has a what looks like a shear top and bottom layer. Look closely at the batting you are considering. I have seen some fabulous poly battings . One advantage ( other than no shrinkage) is that quilts made with a poly batting take so much less time to dry.
I use both cotton and poly battings , it just depends on the project.