Which model? Does you engine have a side PTO for the power drive? If so, forget the Honda - they have their own (peculiar) ideas about auxilliary PTO drives, and it won't fit your chassis - besides, if the Briggs lasted 34 years, the 'extra' reliability is not going to be an issue......
If there is no power drive, any newer engine from Briggs or Tecumseh will fit subject to the correct crank length. If there IS a PTO, the choice is still Briggs or Tecumseh, but probably used, as neither have made a side PTO engine for many years. Another option is to get a new engine from the same model series as your existing engine, and swap the sump pans and camshafts with the PTO drive components.
Are you sure your existing engine is a write off - there's not much that can't be fixed on a Briggs.
phil_saunders(a)bigfoot.com
Phil Saunders, July 2009