DNS, which stands for Domain Name System is one of the most important components of a dedicated server. In fact, DNS is so important that the Internet itself would not function without it. If your dedicated server lacks DNS, no one but you will be able to reach it. The question up for debate is whether DNS is so crucial you would rather let an experienced third party provider handle it, or whether DNS is so crucial you would not trust a third party to do it right. As with any debate, there are two sides to the argument.
Local DNS gives you complete control, flexibility, and certainty over how your records are managed and distributed. By hosting your own DNS, you know exactly what you want, and the only one you have to trust with making sure it works correctly is yourself.
Using a DNS provider often gives you the ability to have additional features and redundancy you may not be able to afford. It also requires less technical knowledge and eliminates the need to manage a DNS server, which can sometimes be a headache. The downside of third party hosting for DNS or any other service is that you are at the mercy of the provider. If you decide to go with this method, make sure they are reliable and secure.
Ultimately, it depends on your preference and technical capability. If you have the knowledge and technical staff to run your own DNS, you will probably want to keep it in-house. If, however, you want features but cannot create what you want on your own, third-party service providers may be what you need.