Whether synthetic is better oil or not is a matter of opinion. HydroGear themselves said to run "Conventional" in their drives as man00 already stated and who better would know what to run than them/the manufacturer.
Depending on it's application it's use, (synthetic) can be beneficial in colder or hotter temperatures. As far as a drive unit on a lawnmower goes there is no real benefit I can see.
You say Ferris, Gravely and Hustler in their Super Z HD recommend Mobile One 15W-50 and maybe they do and I'll have to pull some PDF files/manuals and check just out of curiosity. Toro also says you can use the Mobil 1 15w50 but they also say if you select that type changing the 15w50 or 20w50 synthetic oil should be done every 250 hrs while the oil they recommend you use can be changed every 500 hrs so I don't think at least for me it's very beneficial to run 15w50 synthetic. I'll stick with what the manufacturer says or recommends.