An Algorithm with a lower time complexity will always take a shorter amount of time once the problem size grows large enough. You could run one algorithm on a modern cpu, utilizing Simd and tune for cache coherency and the other in QBASIC on an old 386 and the O(n log n) algorithm would still terminate earlier than the O(n^2) one past a certain n.
the problem is that while dropping from n^2 to n log n is a big deal, dropping from (n log n) to n won't help much if you end up increasing the constant costs at the same time.
