It looks as though it's possible to use instrumentation profiling on an Azure Cloud Service application, but I'm not seeing a way to do the same with an Azure App Service. The only options I've found allowed sampling
profiling.
What methods are available for instrumentation profiling of an Azure App Service?
The Azure Service Profiler is now available as part of Application Insights. It does work with App Services. You can read my review about it here to learn more:
https://stackify.com/azure-service-profiler-review/
It works well with ASP.NET web apps. It can help you find slow methods and stuff going on in your code.
We have the performance testing tool of Visual Studio Online integrated into Azure App Services. Checkout the blog about Performance Testing on Azure App Services.
We also have Remote Profile on Azure App Services now, Check this blog out for more details on Remote Profiling
There is a good Azure Friday Video on Remote Profiling on Azure App Services as well, Check the video here.