The differences between Power BI Service and Power BI Report Server are well documented in the Planning a Power BI Enterprise Deployment whitepaper and the online documentation. The whitepaper by Chris Webb and Melissa Coates also includes a comparison between Power BI Service and Power BI Report Server (Jun 2017 version). Because this is a lot of information, I’ve summarized the most important topics.
Power BI Report Server – two options
Power BI Report Server is the Power BI on-premises alternative to the cloud-based Power BI Service. There are two ways of acquiring Power BI Report Server: 1) Purchase a Power BI Premium Subscription or 2) by making use of your SQL Server Enterprise Software Assurance license.
I use Power BI Report Server. It’s not perfect, but it does what I need it to do and it doesn’t cost the company anything extra (due to Enterprise Edition + Software Assurance).