We have a number of the Mayfair(Bemis) 148E2 soft-close wooden seats, and like them very much, and we also have the Toto SS114.
In reading many reviews of both seats, and comparing those reviews to the products in our home, I can say that "sturdy" is clearly in the eye of the beholder.
I myself find the SS114 to be very "sturdy" if "sturdy" means durable. It's a nice thick piece of solid plastic, and the hinges are durable. That said, it's supposed to have some flex and it does. The flex is why people like plastic seats. If they don't want flex, then the wood seat is better.
The Mayfair seat has refined its attachment method a number of times; the current attachment setup has two nylon bolts that mount from the underside of the toilet and are designed not to move around. You then "clip" the hinges onto these bolts, and the thing stays rock-solid where you mount it.
The SS114 is a more traditional bolts-down-through-the-holes mounting system. This setup could conceivably allow the seat to move around if it's not properly-secured or the toilet doesn't have little indentations in the china to more-precisely center them, as my Drakes do, for example.
Mount the seat right, and don't add a lot of lateral torsion to it when mounting and dismounting your throne, and it should be fine. If it starts to move, tighten it up, like you would any other seat.