In the worst-case situation, a binary tree sort that employs a self-balancing binary search tree requires temporal complexity of the kind O(n log n). Is this approach much more sluggish than merge sort?

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Merge sort

Merge Sort recursively sorts a given collection of numbers or elements by using the divide and conquer strategy in less time. It is one of the most used algorithms, with the worst-case time complexity of O (n log n). It was invented by John Von Neumann. The algorithm continuously divides an array into sub-arrays until each sub-array consists of a single element. It then merges those sub-arrays to produce a sorted array.