Have you tried in the Azure Pricing Calculator the pricing of Azure SQL DTU-Model? It does not have licensing costs, and it is called "budget friendly" for a reason. It is really cheap.
In terms of performance both offer great performance, but Azure SQL Database offers even better performance. Premium tiers and Hyperscale offer integrated high-performance storage, and you can scale CPU and storage separately. Azure SQL Database can scale IOPS based on the workload and that can be very cost-effective.
In terms of scalability, both allow for flexible or dynamic scale based on workload demands.
If security is your top priority, Azure SQL Database might have a slight edge due to its comprehensive security offerings. However, both services are highly secure and compliant with major standards/regulations. Both offer network security, in-transit and at-rest encryption, However, Azure SQL Database offers more advanced security features like Always Encrypted and Advanced Threat Protection. Advanced Threat Protection (ATP) provides a unified package for advanced SQL security capabilities, including vulnerability assessments and threat detection and Always Encrypted ensures sensitive data is encrypted and decrypted only within the client application.
In terms of integration, Azure SQL Database offers more extensive and native integration with a broader range of Azure services, making it a strong choice for complex, enterprise-level applications requiring deep integration. Azure SQL Database integrates better with Azure Data Factory, Azure Functions, Power BI and Azure Synapse. Azure Database for MySQL integrates well Azure Kubernetes and Azure AI Services. Both database options integrate well with Azure App Service.