Methodology vs Framework
A lot of people even experts mix between project management methodology and project management framework. Being aware of the terms and their exact definition is very important and actually essential in any discussion you have as you and your partner, stakeholder, the client will have the common language and you will be standing on the same level.
I don't see it as methodology vs framework and I believe it is a matter of how and when and what do we really want to say by using methodology or framework.
To make things clear we will extract the difference between methodology and framework from the source and we can then decide
In the PMBOK guide, sixth edition, PMI clearly defines the PMBOk and methodology as " project management body of knowledge (PMBOK) as a term that describes the knowledge within the profession of project management. the PMBOK guide is different from methodology: the methodology is a system of practice, techniques, procedures, and rules used by those who want to work in the discipline.
The PMBOK guide is a foundation upon which organization can build methodologies, policies, procedures.... needed to practice project management.
PRINCE2 - is a structured project management methodology. PRINCE2 (PRojects IN Controlled Environments) is a process-based method for effective project management. PRINCE2 is a de facto standard used by the UK Government, widely recognized and practiced in the private sector in the UK and internationally.
Shortly, framework depends on the doer to determine the way to get things done while methodology tells us what, when, how to, and the reason behind doing it. On the other hand Project Management framework defined as "PM framework is a structured collection of all relevant knowledge on how to make change methodologically. It doesn’t describe an exact algorithm of how to manage a specific project but it provides a broad overview of various and different methods, rules, processes, and standards. In this regard, project management methodology can be defined as a level of PM framework."
A good example of a methodology is PRINCE2, while PMBOK, Agile, and waterfall can be considered as frameworks
Read this great article Why You're Confusing Frameworks with Methodologies