Having been the former autocross chair for the Mid-Atlantic chapter of NASA, I completely agree with Shawn's statements.Nasa classing for autox leaves a lot to be desired. It is based on their TT classes for road racing.
It may reflect road course times well (I don't know) but autox times do respond to the same mods with the same types of time gains as road racing and some of the cars seem oddly classed based on how I know they can do in AutoX.
As for NASA vs SCCA it depends more on the local people running the events than the national organization behind them.