Verisign Public DNS is a free DNS service that promises better connection times, stability, security, and privacy when compared to the majority of public DNS services available on today's Internet.
The DNS services that Internet providers offer are often not the fastest, and it is easy enough to verify that by running programs like DNS Benchmark which test the performance of multiple DNS servers on the host system to find out which performs the best.
When it comes to third-party Public DNS services, there are plenty to choose from. While speed and reliability should definitely be a point of consideration, there may be others of interest including privacy, restrictions and extras that services may offer.
Companies may sell data that they collect based on your computer's look ups, and others may redirect you to custom error pages with their ads on them instead of the web browser's default error page.
While it is easy enough to find out about custom error pages, whether a company is selling or processing your data may not always be that obvious.