IMO, cost of searching AVL has O(log n) in all cases whereas in a sorted heap BST it has O(n), O(log n), and O(1) for Worst, Average, and Best cases.

Similarly, for inserting and deleting u need to do it taking a heap or a linked list. This may be ur assignment but dont trust my answer 100%! Rather include 1 example and show the algo analysis in a tree.