Well, they do run "different" carbs and the losi one lists the venturi size, but the dynamite one doesn't.
Silver (green):
http://www.horizonhobby.com/Products/Default.aspx?ProdID=LOSR1064
Gold:
http://www.horizonhobby.com/Products/Default.aspx?ProdID=DYN0909
If you look at the parts explosions, many of the parts are different part numbers. The only ones that are the same are the main bearings and carb cinch assembly.
The con-rod for the losi branded engine is more knife edged than the mach version.
To be honest, I've heard/seen the muggy mach and LST2 mach both in LST2's and they do perform differently. The muggy mach seems to have more high end power and a greater RPM range than the LST2 mach. The LST2 mach seems to have a bit more punch in the very low end.