Anzaniste,
If I am reading your question properly, you are referring to circumferential split collar clamps. Correct?
If so, then the advantage usually lies with the dual-split, 2-screw version. The reason is that you can more accurately match the true round shape of the shaft and still make longitudinal adjustments. With a single-split, 1-screw version the form taken defaults to a slight clearance between the collar and the shaft to allow longitudinal adjustment. When clamped, you only (usually) get three points of contact between the collar and the shaft which reduces the overall area of contact over which friction works.
Hopefully I have answered the correct question.