the criterion of "number of visitors" in this matter I think not the primary.
The main criteria is performance (when Your project starts to slow down on shared hosting, or creates a serious burden because that starts the problems of other clients and You simply are asked to leave), price (large amounts of traffic from a dedicated server are often more profitable than shared hosting), security and reliability (sometimes for greater reliability and security, and for projects with dozens of visits per day from a dedicated server to take).