I have both kinds. I have an old, non-self-healing mat that I've have for at least 30 years that has seen everything. At one time, it was even the kids messy mat. Now I use it to square up quilts because it's so big. I also have 2 self-healing mats: an Olfa rotating cutting mat and a large, Omnigrid mat. I use both of them regularly. The Olfa's surface does not heal as nicely as the Omnigrid, but I love that it rotates. I wish I could repair it some way.
~ Cindy