REMEMBER: with this type of question it is not so much WHAT you say but HOW you say it.

Therefore you don't have to write exactly what is suggested here -
you can argue your own case.
However, try and adopt this style.

Korean War 1950-3 vs. Cuban Missile Crisis 1962

Both were extremely significant, since they were the two main flashpoints of the Cold War, however, the Cuban Missile Crisis was more important, because of just how close the world came to nuclear war.

The Cuban Missile Crisis was more important as the USA and USSR came within minutes of nuclear war.  When on 19th October, U2 spy planes discovered that there were long-range nuclear missiles on Cuba East/West relations deteriorated dramatically.  This was because not only could every city in the US (except Seattle) potentially be destroyed within 5 minutes, but also because the USSR had lied having previously promised not to do this, This crisis was doubly significant, therefore, because of the direct threat to the USA and the breakdown of trust. The crisis deepened further when Kennedy ordered a ‘naval quarantine’ on Cuba (a blockade would have been an act of war), and it looked as though Soviet ships would not stop. However, when Khrushchev sent a letter to Kennedy seeking a peaceful resolution on one level the situation looked more positive for the US because the USSR had ‘blinked first’.  However, the crisis remained potentially lethal because there were still nuclear missiles on Cuba, When, several days later, Castro’s troops shot down a U2 plane relations once again were at crisis point as this was a blatant act of aggression.   When this was followed by a far more aggressive letter from Khrushchev, relations looked set to fall into open hostility – i.e. nuclear war. In the end, the fact that both sides worked hard to secure a compromise (the withdrawal of missiles from Cuba in return for a later withdrawal of missiles from Turkey by the USA) actually demonstrated to both powers that they were both equally determined to avoid nuclear confrontation.  This was important because lines of communication were then established (hotline) and in 1963, the Nuclear Test Ban Treaty was signed.  Therefore during the actual confrontation relations were at crisis point but as a result of it relations thawed.

The Korean War, on the other hand was less significant.   Certainly at various points the crisis looked very damaging.  For example, when North Korea successfully invaded South Korea relations deteriorated because there was a fear that the spread of Communism might cause a ‘domino effect’ that would upset the global balance of power.  Also when China entered the war at the point that UN forces successfully fought back into North Korea it looked as though the conflict might escalate into a much larger war.  However, the fact that General MacArthur, (who wanted to use the atomic bomb), was removed by Truman, demonstrated that America was reluctant to engage in nuclear war.  Also, when the armistice was signed after Stalin’s death, the division of North and South Korea was roughly along the 38th parallel, which meant that there had been no change.  On the other hand, it was the first real armed conflict in the Cold War, (4.3 million lost their lives) and the fact that UN troops pushed across into North Korea (Pyong-Yang became the only Communist capital to be taken during the Cold War) was significant because the US had gone beyond the Truman Doctrine of ‘containment’ of Communism.

Overall, although Korea was extremely important as it could quite plausibly have triggered a global nuclear war, the Cuban Missile Crisis came far closer to doing so as nuclear weapons were assembled and put on standby and is therefore the more important event.