One other thing I failed to mention is in an AR-15 compared to a Remington 700 you have a much more straight line stock configuration. This requires higher rings to get a proper field of view from your scope, regardless of size. With a 700, depending on stock configuration, your cheek weld is usually much higher in relationship to the centerline of the bore, allowing the use of lower rings. In all of my Remington 700's I've always been able to get a good sight picture using the lowest rings I could get away with. As long as the front objective lens cleared, I was good to go.
The only other thing is if you go to a 20 MOA tapered base. This will cause the front objective to drop lower because of the downward tilt of the base. The longer the scope, the worse this condition will be. Sun shades and scope lens covers add to the lack of clearance with tapered bases. This can require higher rings to offset that difference.