An NC Mini will be faster than an Nb Mini if built properly. They are allowed aluminium doors and boot plus perspex windows. They are also allowed a wider track and flares that should make them handle better. These should be built as an English Cooper S from the late 1960s as the Aussie cars with wind up windows are way too heavy.
Nb cars are more the original look of the road going Cooper S. There is still a lot of modification to engine and gearbox etc but most of it is similar to what hot road cars run but a bit more extreme.
Like Chris I have to declare being biased to "the other side"as I run an Nb Mini.
Nb is pre 1965 which was basically the heyday of the Cooper S before the Muscle cars began to come on strong. Nc is pre 1972 by which time the Mini was starting to feel it's age against the other cars such as BDA Escorts, RX2's, BMW 2002s, Porsche 911's not to mention the monster Stangs and Camaro's.
Check out the photos from Muscle car Masters on the net and work out which grid you would prefer to be in. They do a good Nb/Nc split that shows a good representation of the classes.
The question of genuine cars is usually a bit about chest beating (not you Roger

You should not run genuine Cooper or Cooper S shells in Group N. The few that have survived should be preserved. You will eventually have an accident in Group N and you are better to write off an 850 than a Mini Cooper!