Actually the differences in Bhp are almost completely due to the ECU. The different exhaust gives probably no more than 1 or 2 Bhp extra.
Oh and the One's output is actually 100 bhp and not 90 (see "essentials / superchips test drive" at the top of this page). It's frequent to see that factory given power figures are not always true (with many manufaturers). In this case I suspect they wanted to better distinguish the two cars, to justify the price difference. I'm pretty sure there are no "physical" differences in the engine.
The One is significantly torquier at low revs, and the Cooper is "revvier" above 5,000 (but lacking in torque below 4,000).
Frankly, bar track days and "sporty" driving on country roads, the One is more usable for everyday driving. Except it doesn't have the rear anti-roll bar ...
And that's definitely a plus on the Cooper.
I don't need the stiffer and lower suspension; I don't need the bigger wheels. Because they both make the car more uncomfortable than necessary. (Even on impeccably smooth Swiss roads I find myself avoiding the small bumps). But an anti-roll bar for the rear would have been nice, thank you. The One does roll a bit if you start cornering hard.
Does anyone know if this bar can be fitted as an aftermarket add-on? i suspect it would be expensive though...