Difference between red-black trees and AVL trees

AVL trees maintain a more rigid balance than red-black trees. The path from the root to the deepest leaf in an AVL tree is at most ~1.44 lg(n+2), while in red black trees it's at most ~2 lg (n+1).

As a result, lookup in an AVL tree is typically faster, but this comes at the cost of slower insertion and deletion due to more rotation operations. So use an AVL tree if you expect the number of lookups to dominate the number of updates to the tree.

For small data:

insert: RB tree & avl tree has constant number of max rotation but RB tree will be faster because on average RB tree use less rotation.

lookup: AVL tree is faster, because AVL tree has less depth.

delete: RB tree has constant number of max rotation but AVL tree can have O(log N) times of rotation as worst. and on average RB tree also has less number of rotation thus RB tree is faster.

for large data:

insert: AVL tree is faster. because you need to lookup for a particular node before insertion. as you have more data the time difference on looking up the particular node grows proportional to O(log N). but AVL tree & RB tree still only need constant number of rotation at the worst case. Thus the bottle neck will become the time you lookup for that particular node.

lookup: AVL tree is faster. (same as in small data case)

delete: AVL tree is faster on average, but in worst case RB tree is faster. because you also need to lookup for a very deep node to swap before removal (similar to the reason of insertion). on average both trees has constant number of rotation. but RB tree has a constant upper bound for rotation.

Quoting from this: Difference between AVL and Red-Black Trees

RB-Trees are, as well as AVL trees, self-balancing. Both of them provide O(log n) lookup and insertion performance. The difference is that RB-Trees guarantee O(1) rotations per insert operation. That is what actually costs performance in real implementations. Simplified, RB-Trees gain this advantage from conceptually being 2-3 trees without carrying around the overhead of dynamic node structures. Physically RB-Trees are implemented as binary trees, the red/black-flags simulate 2-3 behaviour.

by definition, every AVL is therefore subsets of Red-Black. One should be able to color any AVL tree, without restructuring or rotation, to transform it into a Red-Black tree.

AVL trees are often compared with red-black trees because both support the same set of operations and take O(log n) time for the basic operations. For lookup-intensive applications, AVL trees are faster than red-black trees because they are more rigidly balanced. Similar to red-black trees, AVL trees are height-balanced. Both are in general not weight-balanced nor μ-balanced for any μ ≤ ½; that is, sibling nodes can have hugely differing numbers of descendants.

From the Wikipedia Article on AVL Trees

The max height of the trees is the paramount important to keep balance. It almost equals 1.44 * log(n) for AVL, but for RB tree, it is 2 * log(n). So we can get the conclusion that it is better to use the AVL when the problem is search incentive. What matters is another question for AVL and RB tree. RB tree is better than AVL when facing the random insertion at the lower cost of the rotation but the AVL that is good to insert the ascending or descending datas. So if the problem is insertion incentive, we can use RB tree.