I’m wary of the word ‘definitive’ as all methodologies/philosophies are open to continuous debate and evolution (e.g., consider how little consensus we have regarding economic policy).
That said, a couple of thoughts.
I think that most practitioners would argue that both agile and waterfall have particular strengths – agile is better at responding to change while waterfall works better when consistency is the key goal. Many might argue that agile is more reflective of the real-world conditions most often encountered so its ‘better’ but it really depends on your specific situation (and elements of both can be applied in some circumstances).
In terms of validation, various surveys of software developers have found that those practicing iterative approaches like agile enjoy greater success. These reports include the Standish Group’s CHAOS reports as well as surveys undertaken by publications like Dr. Dobb’s Journal.
With any survey, there is a lot that you can quibble with so I hesitate to say definitive, but there is a lot of consistency in the results regarding the advantages of agile or iterative approaches.
Within agile, there are number of disciplines, such as test-driven development and continuous integration, that you can look at in terms of quality improvements. Not sure if that’s a focus or not. This also points to the fact that Agile is an umbrella methodology so need to be careful about comparing apples with oranges (which specific configuration is being used?).
Ultimately, the strengths and weaknesses of each approach are fairly well documented. As such, the best approach is probably to map these results against your criteria to determine which is the best fit for your organization. Subsequently, you can pilot new approaches to see how they compare with past performance. This is the approach that many of our clients are pursuing and they’re very comfortable with the results.