Azure Dedicated HSM is the appropriate choice for enterprises migrating to Azure on-premises applications that use HSMs.
Dedicated HSMs present an option to migrate an application with minimal changes. If cryptographic operations are performed in the application's code running in an Azure VM or Web App, they can use Dedicated HSM.
In general, shrink-wrapped software running in IaaS (infrastructure as a service) models, that support HSMs as a key store can use Dedicate HSM, such as Application gateway or traffic manager for keyless TLS, ADCS (Active Directory Certificate Services), or similar PKI tools, tools/applications used for document signing, code signing, or a SQL Server (IaaS) configured with TDE (transparent database encryption) with master key in an HSM using an EKM (extensible key management) provider.
Azure Key Vault is suitable for "born-in-cloud" applications or for encryption at rest scenarios where customer data is processed by PaaS (platform as a service) or SaaS (Software as a service) scenarios such as Office 365 Customer Key, Azure Information Protection, Azure Disk Encryption, Azure Data Lake Store encryption with customer-managed key, Azure Storage encryption with customer managed key, and Azure SQL with customer managed key.
Source: HSM FAQ