I think the answer depends on the nature of your borders. I've quilted several quilts in sections, using different techniques. When the wide outer border was pieced (e.g. piano keys), I added the border before piecing that section. (I also had a narrow inner border, but it didn't matter if that one had a couple of seams in it.) However, if your outer border is solid or a small print, and you don't want to see seams in it, then add and quilt it after quilting the center.
Machine Quilting in Sections, by Marti Michell, was a big help to me in deciding how to partition a large quilt.