I tried a side-cutter once, and I kept collapsing the sides of the cans. Without that bead around the top, the side of the can loses its rigidity and the sharp edge moves from the lid to the can itself. shrug - I've never had problems with the sharp edge of the lid, and I've found no advantage to a side-cutter. Clearly my mileage varies, and yours will, too.
I now remember why I moved away from side-cutters a long time ago.