My father used to use the spring tooth harrow on fall plowing -- by the next spring, the fall plowing had hardened up and wasn't so easy to disk -- the disk wanted to bounce along the top of the fall plowing. We would first use the spring tooth and then disk the fall plowing. The spring tooth was much better at breaking up the fall plowing.
Spring plowing was much softer and we would just disk that before we planted. FWIW -------