I prefer the Weaver or Weaver style bases over the Redfield/Leupold style. I just feel they are a stronger system. Although to be honest I've never had any problems with the other style.

As far as rings I've never cared for the Weaver rings. I'll go along with bigbulls on that one. They can damage your scope and it can be a pain to tighten them while keeping your crosshair level. I prefer a Weaver style base with Burris or Millet rings. I use this combination on all my rifles from my target rifles to my hardest kicking magnums and have never had a problem.