I've been following this for a year or so before quads became the 'new thing'. A surf shaper Carl Ekstrom is doing it for years and sparked my interest particularly the quad/twin fin config.
Whist this config allows you the bigger arc + driving bottom turn and the snappy top turn it is really a matter of individual style, this style was once popular. The popular contemporary style is a snappy square bottom turn to a snappy vertical in-the-pocket hack which needs a tight arc both bottom and up. This as the turns are pretty similar the rails and fin setup have been made similar also, hence the symmetry. Plus symmetrical boards are handy for winter NWers in WA!
I haven't sailed an assy yet and would love to try one based on the above.
Ultimately, it is a matter of compromise. Don't buy into a quad/twin/single/assy because its 'better'... its not. Its just different, with each having their own +/- characteristics. The best shape is the one that suits your own style.
Website:
http://surfboardsbyhydrodynamica.com/hulls/ekstrom