What’s the best software development methodology for enterprise-level projects?

We use Scaled Agile for large program and projects. Scaled Agile works very well for managing multiple projects under a program which are inter-related and dependent among each other. We do quarterly planning by conducting Program Increments (PI) Planning event where we put together business priorities, scope for each sprints and key deliverables. We look at load and capacity and adjust the scope accordingly. This is for large programs with 200-300 people in the team globally.

For smaller projects, we use Agile Scrum.

XP – Extreme Programming.

Seems like I can't select any of these... :(

For enterprise level projects the best fit methodology is often a hybrid Agile approach combining Scrum for iterative development with elements of SAFe or DevOps for scalability and governance. This ensures adaptability, continuous delivery and cross team collaboration across large systems.
Technical practices like CI/CD, automated testing and microservices architecture align well with this model. Leading engineering teams such as those behind digital transformation platforms at CONTUS Tech frequently adopt this hybrid methodology to deliver scalable, secure and high-performance enterprise solutions efficiently.

This is a somewhat loaded question : - )!  Agile Scrum is excellent. The challenges I can see are ensuring there is scope management and adherence to that and timelines--- so I'll say agile but I would add, Hybrid. Use some sort of scoping management that might "feel" a little bit like Waterfall. Don't do waterfall on its own. Agile allows for ongoing edits, changes and validation to avoid building something you don't like and tons of rework. It is also great for buy-in and alignment. There are tons of folks well educated in Agile-Scrum. I've seen some also use Agile-Kanban. I don't think anything prohibits you doing a prototype as part of the Agile process. I've experience with large software development projects as a business owner and executive and consultant.