How big a deal is it to take a motor off your old Lawnmower and put it on another?

How big a deal is it to take a motor off your old mower and put it on another? The body has totally rusted out on my snapper but the motor is still strong. Can I use any brand base, My mower has a 6.hp Briggs and Stratton on it. Figure if I can find an old one that still is in good shape but motor sucks, I can do it....any help will be appreciated.