Is it more important to have perfectly tracked projects or projects which
ship 20% faster?
It's far more important to have perfectly tracked projects. A perfectly tracked project which is guaranteed to deliver on a particular day is gold. It makes planning for the rest of the organization much easier.To use a programming analogy, it's like the difference between latency and jitter for real-time systems. Many real-time systems will happily sacrifice considerable amounts of average latency, in order to minimize jitter. It's far better to have a process that completes in 200 ms every single time than it is to have a process that completes in 2ms most of the time, but, occasionally takes 2000ms.
Similarly, from a managerial perspective, it's far better to have a team that gives you good visibility, allowing you to plan for a completion date (even if that date is farther into the future than you'd like) than it is to have a team that mostly finishes projects quickly, but occasionally bogs down and takes a year to finish a project that was initially estimated at two months.
The problem is that far too many organizations have neither. They don't have visibility, and they finish projects late. For these organizations, your dichotomy is a false one — better tracking is how they will ship faster.