I did quite a bit of research on this when I was looking for a replacement element for my previous MINI, a 2004 build One. From what I read, cotton filters are better than foam. I can't remember the exact reasons, but that definitely seemed to be the case. So, I'd say K&N.
In contrast, I've now got the
JCW Sound Kit on my Cooper, and I believe they fit a Pipercross element. If it's good enough for
JCW...
I think at the end of the day, both will be better than the standard paper element, with probably not a great deal between them.
I'm not sure about the 2001 model year, but I don't think there were any changes to the air box between 2001 and 2002. The only change that I know of was on the facelift when they changed the shape of the box (I believe due to the convertible having to have a different shape, and so they made this change across all models to save money).
