Look at the link below, a comparison of the stuff contained in the JCW packages for Cooper and Cooper S.

When I compare the detailed parts lists of the JCW kits closely, one item of interest is that they use the stock airboxes in both instances, but only replace the air filter in the standard Cooper kit.

I've read numerous articles and dyno run results about how replacement filters increase horsepower. That part is clear; however, a couple of contrary opinions on their use are shown here,

I find it very interesting that JCW left off the replacement filter on the S version, particularly when you would expect better horsepower results from a filter replacement on the S vs. the standard Cooper. I wonder why. Is filtration is that much more important that they were willing to go without it even at the risk of some substantial power gains (to protect the supercharger)?