어둡다 means "dark in the sense of having very little or no light, (figuratively) not easy to recognize"
e.g.
어두운 방 dark room
어두운 하늘 dark sky (due to dark clouds)
밖은 벌써 어두워졌다 It was already dark outside.
귀가 어둡다 be hard[dull] of hearing
눈이 어둡다 be weak in (eye)sight
새 means "dark in the sense of approaching black in hue, deep"
e.g.
새파란 하늘 the deep-blue sky, clear blue stky