When speaking about Quality, the PMBOK6 points out that the main methods used are PDCA (PLan-Do-Check-Act) and Six Sigma. In the findings of the book "Tactical Management in Complexity" it is also evident that the PDCA framework is also used to measure quality, but in this case, the quality of the information flow inside the managerial system.
In practice, I have witnessed the need to implement numerous metrics in project management in order to ensure the quality of the project. It is my believe that exactly the measures for quality in any project and in the tactical management as well are generated through the findings and recommendations during the working process. If we discuss about roles definition, the tactical manager seems to pay attention to the flow of information and its quality, and the project manager is collecting, monitoring and interpreting the information in order to update and improve metrics and contribute towards system improvement. This is quite bold statement made by me, but it only opens new gates for further research.
Photo source: Book "Tactical Management in Complexity"