Batting have come so far in the last decade or more. Poly was not such a great choice till they started bonding the fibers. The old poly bats would have fibers that would migrate through the weave of the fabric on the top and then cause bearding. Check your poly to make sure it has bonded fibers or some have a layer of thin , what looks like sheer interfacing on both sides .
Poly is a very exceptable batting , it dries quickly , does not shrink , is warmer, and costs less. It is lighter in weight, and some prefer the weight of cotton. I have great luck with the blends that are out there . Maybe try a new batting on a smaller lap quilt and see if you like the way it performs before using it on a larger quilt.