Some common factors to consider when electing a strategy for the upcoming project.
• Size of the project
• Clients or stakeholders, external and internal
Projects suited for a Waterfall methodology
• Projects that need direct designing and in-depth documentation
• Projects with a fixed scope, time and budget
• Best for straightforward, unchanging projects (legacy)
• Sequential/linear stages
• Projects with an absent client
Projects suited for an Agile methodology
• Projects where your organization is responsible for the whole process
• Continuous cycles
• Projects with flexible evolution
• Larger, undefined, complex projects
• Projects with client involvement (customer focus)
When determining the methodology to use, an organization should initially address the points above in order to know the proper approach that may match the legacy system(s), and upcoming projects.
From my personal experience, I even have seen that the toughest challenges in transitioning from Waterfall to an Agile methodology is that the Product Owner will have a tough time changing his/her mindset of “owning” a specific deliverable till it's handed off, as opposed to working on each deliverable conjointly.
As a Scrum Master, I am always going to say that the true strength lies in people working together towards a common goal regardless of the chosen methodology.