SSRS is part of the Microsoft "BI stack" and is part of SQL Server. When you install SQL Server you have the option to include different parts of the BI stack including SSIS, SSAS and SSRS. You can, in part, manage SSRS from SQL Server Management Studio as it's very integrated with SQL Server. SSRS runs as a service on a server you control (either a local physical or virtual server, or in the cloud). SSRS is free when you have a SQL Server license.

Power BI (which I have never used and don't know much about) is cloud based and is part of Microsoft Office 365. It runs in the cloud on hardware that you have less control over.

I have been working with SSRS for years. What makes it great is how it's pretty solid and stable. I can put together and publish a report in minutes and it will work. SSRS hasn't changed very much which means if you know one version you'll be able to manage them all. SSRS, however is old and tired. It's interface is outdated and crusty, you have minimal control over how parameters behave or appear. You can't use SSRS for slick looking charts and graphs, that functionality in SSRS is very week compared to what's available today.

Power BI on the other hand is extremely slick. The stuff I've seen created with Power BI is pretty amazing. It's certainly more modern and current.

On the flip side, for ever Power BI veteran, there's 20 people with many years of SSRS experience. There's more SSRS material. Note, for example, SSC has a Stairway for SSRS but not Power BI.

That's my 2 cents.