Power BI Report Server and Power BI Premium Service serve different purposes in the Power BI ecosystem, and their key differences can help determine which is the right fit for an organization.
Power BI Report Server is the on-premise solution designed for organizations that want to keep data and reports within their network due to compliance, security, or facility constraints. This includes support for paginated, mobile-ready, and Power BI reports created with Power BI Desktop and optimized for Report Server. Unlike the Premium Service, which provides advanced, cloud-based capabilities, e.g., AI and real-time collaboration, this does not offer such features. Licensing for Report Server comes with SQL Server Enterprise Edition with Software Assurance or part of a Power BI Premium license.
Power BI Premium Service is the same in that it is cloud-based - thus, scalable, hosts more advanced analytics, and carries collaborative features. It adds AI-powered insights, big dataset handling, dataflows, and connections with other Microsoft 365 services to the offerings. Real-time dashboards and features such as automated machine learning make the Premium Service a great option for organizations that make innovation and cloud-first their priority. It is covered under a subscription-based licensing model that features capacity-based pricing.
Power BI Report Server caters to on-premises scenarios and has specific compliance requirements, while Power BI Premium Service is geared towards cloud-centric operations with advanced features for collaborative efforts. It all boils down to what your organization's infrastructure looks like and what features, as well as licensing options, it needs.