Sort of. As you go up the scale the Big-O values are almost always dominant. It's very rare to see a situation where you would choose the algorithm with the h

Sort of. As you go up the scale the Big-O values are almost always dominant. It's very rare to see a situation where you would choose the algorithm with the higher value. However, when two algorithms have the same Big-O there can still be a big difference in performance, especially in the face of how a cache influences things. (There are cases where the memory accesses are so important that they can make the "bad" approach better. A while back I did some time testing and found the Sieve of Eratosthenes inferior to brute force because of all the cache misses.)