Polyester batting does not shrink at all. It tends to give a more "modern" look to quilting lines. Unless it is a really thin batting, it also tends to give more "loft" to the finished quilting.
Cotton batting shrinks (unless you pre-shrink it; not possible with all cotton battings) and gives a more "traditional" look to the quilt -- i.e., a more crinkled look, and a somewhat flatter look.
However, a lot depends on which specific batting you use. There are very thin polyester battings that give a very flat look to the finished piece (often desirable for wall hangings). There are also combo battings.
If you are looking for an all-around high quality batting to start out with, I recommend Hobbs 80/20. It is a good starting point.