From my point of view, these two approaches are not very correct to compare as "approaches" to project management. Because the PMBOK approach is primarily an approach to project planning. By passing through the corresponding "areas of knowledge" in the logic of the process model "inputs" - "tools and methods" - "outputs". As the "outputs" when working with each of the areas of knowledge, the most important is the formation of a "project management plan" by "contributing" to the overall "plan" with its "subplane" - by content, timing, etc.

SCRUM proposes the use of "values" and "principles." You can try to mapping between SCRUM and PMBOK. It seems to me that only Change Management (as part of the Integration Management) will remain, Human Resource Management, Communications Management, Risk Management, Stakeholder Management.

Those. SCRUM is less of an approach to managing all aspects of the project as part of its implementation. It is rather an approach to the organization of the work of the team and communications both within the team executing the project and involvement in the communication of the customer as a "Product Owner".

As the creators of the "flexible technologies" of project management have correctly noted, they (including SCRUM) are "easy to understand but difficult to implement." Having learned the planning in the logic of the PMBOK it will be much easier to work in the logic of SCRUM commands and SPRINTS.

But "Scalable Agile technology of project management" (SAFe, NEXUS, SCRUM of SCRUMs) is already almost a PMBOK ... And even slightly including a part of the content of standards for managing programs and project portfolios ...

Dimitry Spasibo, your view i understand and share for a large portion. Comparing always shows a misfit  somewhere. The main thesis here is: with Scrum you have no requirement for a project manager and the qualities & competencies in the team will drive the result. Mastering scrum is then to serve the team, rather than guide on planning. I am a certified PMP and have noticed during the last 3 years that i benefit more from teh scrum practices and values.......

I trust that more people will react in order to have a sensible outcome. And yes the Scrum of Scrums &  Nexus Framework may show resemblance to a future(?) version of PMBOK.