I prefer a very traditional look on my quilts, therefore I mainly use Hobbs Heirloom 80/20, Legacy 80/20 or pure cotton battinings like Tuscany or Legacy. I also like Wool a lot (Hobbs or Tuscany), it's so easy to needle and the quilt has a little bit more "puffy".
A few months ago I had the opportunity to try Legacy Poly batting for a wall hanging and although I don't like to touch poly battings it was a pleasure to quilt it. No bearding at all, easy to needle and a soft drape! Very nice!
Over the years I have used many different battings and this helped me a lot to find out my personal preferences. I avoid all battings with a "scrim" because I quilt very densely and my stitches are quite small. For me it's impossible to reach this with a batting like warm & natural.