@mcc I think the circular design is probably easier to learn. You can't run off the scale like with a linear design, since it loops back around, and there's only one index to deal with. Since the length of the scale is πd, a circular rule can be much more compact and still have better resolution. The pivot keeps the face off the slide rule off the tabletop, which helps prevent scratches and wear. The cursor is usually designed so it can't be knocked out of alignment, a common issue with linear rules.
On the down side, the inner most scales tend to be more compressed, as you move around the disk the numbers turn upside down, and the front and rear inner disks are not connected which makes duplex-flips a bit tricky. They are also impossible to disassemble for cleaning, and the manufacturing tolerances are tighter.