With Azure, there are multiple ways to host websites – Azure Website, Cloud services and Virtual Machines.
For most web apps, Azure Websites have been the best choice. Deployment and management are integrated into the platform, sites can scale quickly to handle high traffic loads, and the built in load balancing and traffic manager provide high availability. You can easily move existing sites to Azure websites easily with an online migrating tool or create a new site using the framework and tools of your choice.
If you need more control over the web server environment, such as the ability to remote into your server or configure server startup tasks, Azure Cloud Services is typically the best option.
If you have an existing application that would require substantial modifications to run in Azure Websites or Azure Cloud Services, you could choose Azure Virtual Machines in order to simplify migrating to the cloud. However, correctly configuring, securing, and maintaining VMs requires much more time and IT expertise compared to Azure Websites and Cloud Services.
If you are considering Azure Virtual Machines, make sure you take into account the ongoing maintenance effort required to patch, update, and manage your VM environment.