Just as in automobile cam timing, lift, and duration does affect performance. Briggs also would label same engine with different hp ratings even when the engine had the identical specs. This what they and other manufactures got in trouble about here in the USA.
A good example was three opposed engine that came in the shop at the same. There a 18.5, 19.5, and 20.5 hp all with the same model and type numbers.
I also know cam timing does effect hp as I accidentally timed a 12 hp L head years off by one tooth. Boy what an increase in hp I had. I just don't remember if I advanced or delayed it but it is more likely I advanced it a few degrees. So I can personally believe in the increased hp.
Also on some of the larger Briggs they use restrictor plates to limit the hp of a larger engine.