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The filter you linked to is an oiled filter. Many on here are not fans of oiled filters because the oil can get on the MAF sensor and cause issues. AFE does make dry drop-in filters for our cars, as do other manufacturers. I am sure they flow better and therefore make increases in performance over stock (whether HP, torque, and/or MPG) but only slightly. It also has the added benefit of being reusable and should save some $ in the long run but at the expense of more labor for you. I say go for it.
As soon as I got home with my '12 I put the dry filter in. No problems and I think it works great. Coouldn't tell you about any "gains" as I have nothing to compare it to.
i should point out that the vehicle selector search drop down on the afe site does not include the option for the Countryman S the proper link for the S is http://afepower.com/shop/details_new...174&brandID=59 according to the guys at afe. the original link was for the non S model.