One definition of branding is to transform the value of your product into an emotional feeling that people will buy. If you can’t offer a quality product people will stop buying it. So of course function is the core. A beautiful emotional advertising that gives the user another impression of the product (normally a false and better one) is just as bad as a product with functions that doesn’t work.
Even though the function is at the core the successful product has a combination of high quality, functions users wants and an emotional advertising that are in-line with the functional aspects of the product.
Then you have the basis of a success.