what advantage does heapsort has over smoothsort?
Having just done some reading up on the two algorithms, it would appear that heapsort has no implicit O advantage over smoothsort. This kind of makes sense when you think that smoothsort is just a special kind of heapsort, using a special kind of heap.

Where heapsort does have is an advantage is that it is easier to understand, and much better documented. There are very few publicly available implementations of smoothsort, and very little literature on them, however there is a lot of literature on heapsort.

Indeed, the only real accessible literature is this write-up by Keith Schwarz. It is also the basis of the wikipedia article.