The HD6xxxm series has reached peak optimisation and been moved to legacy status, there will not be any further driver updates for your product. More information available here.
The latest Crimson driver for your system is 16.2.1 and is available here.
The last Catalyst driver for your system is 15.11.1 Beta and is available here.
I would recommend using DDU to sweep your system of AMD drivers, and then trying the drivers above to see if they resolve your issue with OSB studio and Xsplit. If the issue continues, you might be better off trying your other system as you can use updated drivers.