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First of all, you are technically required to provide a minimum of two, separate DNS servers. This means GEOGRAPHICALLY separate. Most setups that run a DNS server on a web host just fake this by pointing both NS records at the same server.
Secondly, either the registrar-provided or third-party DNS service is likely to be far more reliable and faster than running your own server. They typically provide a world-wide network of DNS servers, and many providers use IP-Anycast technology to automatically route DNS requests to the nearest server.
Bottom line is, you probably will get both more reliable and faster DNS service by using the free DNS servers offered by your registrar, rather than running your own on your web host.