It's perhaps not rigorously scientific, but our red mine server is tied into our Jenkins continuous integration server, which also has a code coverage tool tied in. We've been doing this for a little while, and have the ability to visualize bug counts divided by severity along side test count, and code coverage percentage.

There is an order of magnitude difference from the projects that did not use TDD, and the projects that did. Another nice part of red mine is that I can also visualize how close we are at meeting our expectations for time estimates (they have this task tracking feature). Overall adding TDD has made development a bit slower in the front end, but a lot shorter in the back end (during QA). However when you look at the past, it would seem like something like 60% to 70% of our time was actually spent fixing issues found in QA, which was usually under estimated. So overall we're definitely seeing quantitative proof that TDD is a better methodology in comparison to our past process.

Anther cool tool for project management is we've built a set of tools that allow us to designate a requirement from our functional spec with a unit test, which runs every check in. So our project manager can get a near real time assessment of our progress. I also use that report and associate it with the code coverage report. Though this part of the system is newer, so I have no data on how effective it is.