After reading both papers, I have to disagree. Chain of Draft seems "identical" to Concise Chain-of-Thought (CCoT) https://arxiv.org/abs/2401.05618. Additionally, the CoD authors seem to mention that it is cognitive inspired but don't give any actual basis for that.
Sketch-of-Thought, while similar in terms of its goal, seems to be based on cognitive science principles and has better extensibility than CoD and CCoT (they basically just say "answer in X words" and leave it at that).