Where I live butter is butter, it all has the same fat content. Unless you get 'spreading butter' which has other stuff added to make it softer, but that's really not used for baking. Then there's salted or unsalted of course. I've never heard of getting a higher/lower fat content butter to make soft cookies.
Commercial butter in the U.S. is 80% butter fat, so brands will not make a difference in that respect. However, butter has a lower melting point than vegetable shortening which means the cookie dough will spread more quickly, i.e. you will have a flat, crunchy cookie, not a soft one. So if you want soft cookies use a recipe that contains shortening rather than butter. A higher melting point means the cookie has a chance to rise before the fat melts.
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