Question

Both quicksort and heapsort do in-place sorting. Which is better? What are the applications and cases in which either is preferred?

Answer 1

This paper has some analysis.

Also, from Wikipedia:

The most direct competitor of
quicksort is heapsort. Heapsort is
typically somewhat slower than
quicksort, but the worst-case running
time is always Θ(nlogn). Quicksort is
usually faster, though there remains
the chance of worst case performance
except in the introsort variant, which
switches to heapsort when a bad case
is detected. If it is known in advance
that heapsort is going to be
necessary, using it directly will be
faster than waiting for introsort to
switch to it.