I understand that as of the 2016 versions it is now possible to run SSRS and Power BI on the same server. I would like to know if anyone is currently running this combination and what are the pros and cons of doing so.
I assume you mean Power BI Report Server.
It's useful if you want to test or develop using PBIRS without risking your SSRS installation. As far as i can tell PBIRS can do everything SSRS can and more. You can still deploy SSRS reports to PBIRS. In certain scenarios you may want to have 2 instances of a reports server. The argument would be the same for having 2 instances of SSRS. Separation, security, scalabiliy.
The downside is competition for resources and management/maintenance overhead. I think you really need to have a strong argument for maintaining both. My reccomendation is: Test it, if it does everything you need then replace SSRS with PBIRS.
If you're insterested in how to do that I discuss the steps here: https://dba.stackexchange.com/a/219134/41928