A conventional (note that things become conventional because they work) rig has the nice feature that when running downwind, the jib tries to lift the bow. With a swing rig, the entire rig tries to bury the bow. A hull that works well with a conventional rig might not be as good downwind with a swing rig. Of course, if it was designed with a swing rig in the first place, thats another story.
Arranging controls with a swing rig can be easier, and, since the forces each side of the mast tend to partially cancel, a smaller control device can handle the same sail in stronger winds.