I've done the Bluefin Remap thing on my 'S', but it was specifically for the JCW 210 (it had a thread on here a while back). The One and Cooper are a different thing, so my experiences won't really be applicable. On the 'S', the remap just made the car feel a bit more 'serious', which I got used to and didn't notice after about a week or so. Still think it was worth doing though, as it 'filled in the gaps' on the standard ECU.
As the guys have said, the remap for the 'old' One gives a whole lot more 'oomph' - doesn't it bring the One up to Cooper power levels, as the only difference between the One and Coop was the ECU settings. Or am I remembering it wrong?