Was one far more important than the other, or were the two both looming large in the minds of the Japanese leadership as they discussed the possibility of surrender?
Not to preclude any other great answers you might get on this post, but you might be interested in these past threads that deal with this topic, including "There has been some controversy on the true effect of the atomic bombing of Japan. Was it the bomb, or the Soviet declaration of war that ended WWII?".