The engine is the heart of the vehicle. However, it depends on what percentage the $650 is out of the total cost, and how long you plan to keep it. If you plan to keep the mower for a long time, and the $650 is a small fraction of the total cost, get the Kawaski engine.
Back when Snapper was not owned by Briggs and Stratton, I bought a Snapper rear engine rider mower with a Honda engine for more money but I am very happy with it.
I went with the better engine for more money because I plan to keep the Snapper rear engine rider mower for many years, and Honda engines are very reliable.