Better and Cut above

Better adjective - (comparative of `good') superior to another (of the same class or set or kind) in excellence or quality or desirability or suitability; more highly skilled than another.

Cut above and better are semantically related. In some cases you can use "Cut above" instead an adjective "Better". informal substitute

Better and cut above are semantically related. You can use "Better" instead an adjective phrase "Cut above".