If you hit the limiter in a ONE then it bounces against maximum revs ever so slightly and you lose all acceleration (maintaining speed instead). It actually feels like you hit an impenetrable wall of maximum speed and that everything has gone horribly wrong - not a nice feeling.
Presumably, as it's the same engine, then the Cooper will be exactly the same - you'll just get to the rev limiter faster. I've never driven a CooperS so couldn't tell you about that one.
Hope that helps.
All the best,
Andrew.