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

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. 

Scaled Agile Portfolio - as this Agile for Enterprise programmes with Enterprise portfolio management deliveries. 

Agile directs small sub programme to deliver the enterprise goals

Hybrid mode is often better with a choice of the methodology done by both business and IT at the start of the project

Would be interesting to see what the response would have been if "Hybrid approach (Agile/Waterfall) was given.

There is no one right answer. It depends on various factors including but not limited to organizational size, scale, spread, and overall maturity.