I have experience w/ both of these systems. I prefer the Remington platform. It has proven to be a robust, accurate, and user friendly rifle. My Steyr(a SSG69) on the other hand was a real piece of junk. I could not get this thing to group for the life of me. And another thing is the chamber. The Remington will group any type of ammo fed to it. The Steyr's chamber is set to higher tolerances, and will only use match ammo. I prefer a weapon system that will adapt to what is available, which my Remington will do. No matter if it is PMC match in the red and white box or Federal Gold Match it performs. My Remington built rifle shoots with the accuracy I expect from a custom gun. I found the Steyr to be uncomfortable and it felt strange. The Remington is an old friend that is capable of accuracy beyond most peoples skills. I'm sure the Steyr is a nice gun, but I will be more than happy with my Remington.
Be Safe
Mike