CloudMonix Agent can be installed only on Azure Windows VMs, stand-alone Windows Servers, and Azure Cloud Services (Roles).
The option of using Azure Diagnostics on stand-alone Windows Servers is not available. Therefore the only choice between Azure Diagnostics and CloudMonix agent is for Azure VMs and Cloud Services.
In order to gather metrics CloudMonix has to use either the standard Azure VM Diagnostics Extension or its own Windows Agent. The choice of the agent is important, because there are differences in their functionality.
By default, CloudMonix will attempt to configure and use Azure Diagnostics. However, if more functionality is required, it may be beneficial to install CloudMonix agent instead of Azure Diagnostics.
Specifically, in addition to Performance and Event Logs that are available through Diagnostics Extension, CloudMonix agent can track Windows Services, Scheduled Tasks, Windows Updates, Processes, and custom PowerShell-based data. Furthermore, any automated tasks that need to be executed on the VM, such as PowerShell scripts, Windows Service restarts, etc., need to run via CloudMonix agent.
The detailed information of what metrics and actions are available when using both agents is provided in Azure Virtual Machines (Windows) and Azure Cloud Services (Web/Worker roles) articles.
For detailed installation instructions refer to the How do I add CloudMonix agent to Azure Windows Virtual Machines? and How do I add CloudMonix agent to Azure Cloud Services (Web/Worker roles)? articles.