I own both, Remingtons and Brownings. My Brownings are the original A- Bolts Is, not the newer A-Bolts IIs. All of my Remingtons are shooters - meaning 1MOA or better with at least one factory load. Same holds true for my Brownings. I have never had any problems whatsoever with any of my rifles. My brownings, however, are of better quality in terms of fit and finish, than the Remingtons.
Nowadays, I buy Tikkas (as most members know). If money is not that much of a concern, I buy either Sakos or Kimbers.
Zachary