Both times seem to be described by major powers building up militaries and preparing for a supposedly inevitable war. Did the threat of nuclear weapons cause Cold War leaders to avoid total war at all costs? Wasn't this the case with many new technologies going into WWI as well?
Several differences exist here:
First, Yes the threat of nuclear war was the major deterrent to actual war. Even though the true effects of nuclear weaponry were yet to be understood, these awesome new weapons terrified both those that had them and even more so those that did not. As the Cold War progressed and the USSR and China become nuclear-capable nations and delivery systems advanced, the specter of a nuclear war becomes even more destructive and terrifying. These fears and technological circumstances worked together to create the phenomenon of Mutual Assured Destruction (MAD) in which a nuclear war could not be won, but instead only produce the complete annihilation of all participants.
Secondly, in the late 1940s/early 50s as the Cold War unfolded the world was fresh off the heels of two global wars that killed tens of millions of people and devastated large swathes of Europe, Asia, and Africa. These wars destroyed empires, nations, and entire groups of peoples. As European nationalism subsided in the wake of WWII, many of the reasons behind the World Wars were finally resolved.
Thirdly, the new technologies developed in the years prior to WWI were largely untested in combat by the time the war started. Simply put, most nations could not realistically imagine the new brand of warfare created by the advent of the machine gun and other technological innovations. This is untrue of the nuclear bomb, as its effects were seen clearly in Japan.