As far as I know the time complexity between AVL trees and Binary Search Trees are the same in average case, with AVLs beating BSTs in worst case scenarios. This gives me a
Since there is the added overhead of checking and updating balance factors and rotating nodes, insertion and deletion in AVL trees can be pretty slow when compared to non-balanced BST's.
Because of the tight balancing, search will never take linear-like time, so you'll probably want to use AVL trees in situations where searching is a more frequent operation than updating the tree.