One advantage that the traditional Azure Cloud Services had over Azure Websites was the support for VIP swap. This allowed you to switch your development and production environment with one click. You could deploy your application first to the test environment, check if everything is working as expected and then switch to production. The only difference between the 2 environments is that one is using the ‘real’ url of your cloud service where the other is using an auto generated GUID.
If you wanted a similar experience using Azure Websites, you had to deploy to multiple sites. This has now changed thanks to the introduction of Deployment Slots.
From the documentation:
The option to create site slots for Standard mode sites running on Microsoft Azure Web Sites enables a staged deployment workflow. Create development or staging site slots for each default production site (which now becomes a production slot) and swap these slots with no down time. Staged deployment is invaluable for the following scenarios:
Validating before deployment - After you deploy content or configuration to a staging site slot, you can validate changes before swapping these changes to production.
Building and integrating site content - You can incrementally add content updates to your staging deployment slot, and then swap the deployment slot into production when your updates are completed.
Rolling back a production site - If the changes swapped into production are not as you expected, you can swap the original content back to production right away.
Microsoft Azure warms up all instances of the source site slot before the swap to production, eliminating cold starts when you deploy content. The traffic redirection is seamless, and no requests are dropped as a result of swap operations. Four deployment slots in addition to the default production slot are supported per Standard web site.
Each deployment slot has its own publish settings, so the deployment experience in Visual Studio using Web Deploy remains similar(and also Source Control Integration is still an option).
More information here: http://azure.microsoft.com/en-us/documentation/articles/web-sites-staged-publishing/