Which is better and why?
Azure DNS is a hosting service of DNS domains. It has excellent operating time and performance, resulting in fast resolution. We like the ability to view everything in the Azure portal - this makes things very easy to manage. Azure DNS can detect the change of ISP very fast.
Azure DNS does not currently support DNSSEC, which may be unacceptable for some users. This solution only provides domain and DNS management; many other DNS services provide more. You do have to have some knowledge of coding to use Azure DNS, or it can be very difficult to use. We would like to see improved technical support, with faster response times, and we feel this solution can run a bit on the expensive side.
AWS Route 53 provides both DNS name management and DNS-level traffic and also provides excellent failover services. Amazon Route 53 provides 100% availability, and integrates seamlessly with other AWS solutions. This solution can also be used with non-AWS resources. AWS Route 53 has the Traffic Flow feature, which helps improve your application's performance and end-user reliability. You can easily configure Traffic Flow to direct each end-user to the best location by using the rerouting capabilities. This is one of our favorite features.
The UI with AWS Route 53 can be challenging to learn. If you are in a non-AWS infrastructure, Route 53 doesn’t really offer significant advantages. We would like to see drop-down boxes with improved defaults when setting up a new zone file to make the process quicker. AWS Route 53 does tend to cost a bit more than other DNS providers.
While Azure DNS can be easy to use and deploy very quickly, some features, like DNSSEC support, which many consider an important feature, are not currently supported. Of course, Azure DNS works best in the Microsoft ecosystem, and there are 3rd party add-ons available to satisfy this and some other perceived shortcomings of Azure DNS.
AWS Route 53 is very diverse, robust, and offers excellent scalability, but to garner the best results, it's best to be invested in the AWS ecosystem.
Our feeling is AWS Route 53 does more. If you are not locked into another ecosystem, give it a try.