Means to an end, really. Cloud servers are just VPSes (virtual machines) with a catchy name, whereas obviously dedicated servers are an actual box that you control completely and have exclusive access to.
So the answer really depends on how large your site is and how much grunt you need to run it. Our site runs on a dedi because of the resources we need to make our application work, whereas other forums our size without additional applications would be fine on a mid-spec cloud server. Your mileage may vary.