These units you're referring to are generally looked upon as 'elite' units and demonstrate great pride in belonging to an organization with a very distinct and colourful history. Both the 82nd and the Marines are famous for their heroics and doggedness on the battlefield. It's certainly not my intention to bash the Americans. If that's the way it was interpreted, then i appologize for the confusion.
I think the underlying part of this particular debate was whether or not soldiers serving in a distinct unit with a colourful history, be them Americans or Canadians, would fight better than the average joe. The size of the CF compared to the USMC is irrelevent so i'm wondering why you even brought that up.
Either way, Marines think they fight better than the US Army. Why? Because they're Marines and they're proud of who they are. The Patricias think they're better than the RCR's. Why? Because they're Patricias and they're proud of who they are. They're all good in their own right and they all believe in the particular unit to which they belong. Soldiers need something to believe in other than themselves and their buddies on the battlefield because it gives them cause and propels them forward.
The argument goes both ways and there's really no final answer to the question. There's great points of argument for each school of thought- and that's the fun of having the debate.