What are the "Pros and Cons" for these two methods of mesh-refinement? Both seem to be the prevalent methods.
I can naturally imagine that global red refinement is comparatively easy to implement and attractive for research in multigrid-methods, while NVB is used in AFEM-theory because some attractive formal properties that ease error analysis, and furthermore local adaption with NVB seems easier to implement than with Red-Green-Refinement.