Organic cotton batting is a heavier batting which is meant to be used as a foundation material in upholstery, not as a replacement for dacron/polyester, which is a lighter weight ‘finishing’ layer between the outer fabric and the layer beneath. The wool batting is the correct weight, and is used to replace the dacron/polyester layer.
Polyester batting is glued in place in conventional upholstery. In natural upholstery, instead of glue, the wool batting has a thin spun backing that can be stapled or stitched, depending on the upholstery application. The unbacked side of the wool sticks quite nicely to burlap (the material used on sofa and chair backs as a support layer for the lightweight ‘finish’ batting) and to latex foam.
Please note that wool batting requires an extra layer of ticking fabric between the outer fabric and the wool batting to prevent the wool fibers from migrating through to the fabric surface.