Even though information about cookies can still be found in the site’s privacy policy, this separate disclaimer helps users more easily know about the site’s cookies usage.
Privacy Policies are overall better than disclaimers because they disclose far more information and details to users than disclaimers.
For example, the cookies disclaimer simply lets users know that cookies are used, while the cookies section of a Privacy Policy will typically include information about what types of cookies are used, for what specific purposes, how this will affect users, and steps a user can take for opting out of the use of cookies.