Burris Signature rings are not flat on the inside, but are hollowed out to make room for the Pos-Align inserts, which are somewhat donut shaped on the outside and flat in the center to mate with the scope. They have a ball- joint type movement within the rings.
If you need the Pos-Align inserts to correct sight alignment or gain altitude, the Pos- Aligns are definitely the way to go. To use the Zee rings, you'll probably have to get a Ruger/Weaver adaptor. I don't think Burris offers Ruger- style Signature rings, which is just one more way they've dropped the ball. I am a HUGE Burris fan, but they are like a great halfback with fumble-itis. They could win the Heisman, so to speak, if they'd shape up.
If you are just interested in the Pos-align inserts to keep from marring your scope, there are alternatives. Brownells carries 30mm/1" inserts which could fit inside a pair of Ruger 30mm rings. Chris at SWFA might even sell them also, as I believe he uses them inside his Tac rings... speaking of SWFA rings...
if you decide to go with the Ruger/Weaver adaptors, SWFA carries some robust 30mm tactical rings w/ non-marring inserts to fit a 1"tube. note: I'm not sure if the crosspiece for the base is Weaver or Picatinny, nor do I know how well they maintain a tight grip on your scope. They look like the real hot setup if you want to keep from adding ring marks to your scope's finish, and they are a lot closer to hot- swap removable than the Signature Zee rings, which are a great idea- poorly executed. The Signature Zees mount to Weaver/Picatinny bases in an inappropriate manner, i.e. the ring's base- mount side piece is not removable, but instead must be bent with screwdriver (slotted, no less) pressure to snug up against the base. C'mon Burris!!!
To be fair, Burris' Double Dovetail Signature rings are about as close to perfect as you can get.