What is the source of this information? The UK motoring press (Autocar) reported the torque curves were "almost identical up to 3,500" and then the Cooper's was better. Because of the Cooper's lower gearing, the Cooper has better acceleration across the whole rev range.
What Car? is the only UK magazine to performance test both a One and a Cooper. In-gear times measuring low revs acceleration were as follows
30-50 in 5th gear Cooper-11.7sec One-15.3sec