Simple binary tree is O(n^2) just like a linked list.
Unless you know what you know your distributions and are generally proficient in probability theory (in 99% of the cases, neither can be relied on) the only relevant big-O metric is the worst case one
My favorite example is adding and ordered list of items into a a simple tree, all you've really done is created a linked list. Big-O doesn't know what your data looks like but you generally should.