From my 'book larning' stage, I picked up that another factor is the size of the fat globules. Apparently, Jersey milk is *not* ideal for hard cheese from this point of view - although plenty of folks make good hard cheese from Jersey milk

The figures for butterfat by breed are intriguing. As a hand milker of pedigree (and purebred but not pedigree) house Jerseys, I can say that the apparent butterfat content varies wildly according to stage of lactation, the weather, the season, how the grass has been growing that year, what forage is being fed, what cake is being fed, etc etc etc. The figures are perhaps normalised in some way, perhaps an average from all the milk recordings of all the cattle of that breed, or something.
However, when buying shop milk, you presumeably get an averaged product.
And on that topic, I would personally say that you want to avoid homogenised milk, which has messed around with the fat globules. It's not always easy to find unhomogenised milk these days, so seeking out a local producer is probably a good place to start. And at least one of the Channel Islands milk products is unhomogenised - called Gold Top or something, I think - still has the cream on top
