One of the biggest differences is hyperextension. There is quite
a bit of it in Yoga, downward facing dog is hyperextension of the
shoulder girdle, upward facing dog hyperextends in the opposite
direction.
There is no hyperextension in Pilates, joint stabilization is very
important. Swimming, for example, is pelvic stabilization and
shoulder girdle stabilization, while moving the arms and legs
(withouth rocking).
The ab series of five is done with the trunk in neutral spine, and
stable, while in C-curve, moving the arms and legs in their
joints.
The point is Pilates may look somewhat like Yoga, but the
principals are quite different. Not better, just
different.