Benchmarks of how it beats qsort, Timsort, pdqsort etc.: https://github.com/scandum/quadsort#benchmark-quadsort-vs-st...
Is it called esoteric just because it's complex?
This is the first time I've heard quadsort being called esoteric. It isn't much more complex than Timsort. It is however challenging to port ~1000 lines of code that can be tedious to debug. If you make one simple error/typo you could be stuck for hours in debugging hell.
Hence I recently published piposort, which is ~150 lines and pretty basic, while still offering excellent performance. Not as good as quadsort, but it could make for a stepping stone in a porting effort.
With quadsort, fluxsort, piposort etc., you have an impressive coverage of the design space of sorting algorithms!