The Burris Signature Zee rings clamp by bending steel at a weakening cut, rather than with a separate piece. I have run into situations where they would not slide over a Picatinny base. I have never had the problem with a Weaver base.
On a related issue, I have always found it amusing that so called tactical rings, and their bases are, in many cases secured to the action with four little bitty #6 screws. A chain can never be any stronger than its weakest link. If I had to stick with that size for a big heavy scope, in an application that might see some rough use, I would carefully epoxy the base(s) to the action (but not the screws).