In my experience the closer the stitching the stiffer the quilt. Different battings recommend a maximum difference between the quilting stitches.
I also feel that different battings have different levels of stiffness in them. I have found Hobbs 80/20 cotton blend and Hobbs wool to be some of the softest battings that I have tried. I have used Warm & Natural, and some other pre-packaged brand from Joann's. I have also recently used Quilters Dream Blend and Quilters Dream Cotton. I have ordered a roll of Quilters Dream wool - mostly because Quilters Dream is the only batting the LQS will let me use on their longarm machine. So far I have not been enamored of the Quilters Dream battings. I found both the Blend and the Cotton to be stiffer than I like.