Of course, there is no way to know this for sure. However, I would argue that there would have been little in the way of tangible difference in the way history played out.
If JFK had not stepped up to the USSR, the Soviets would have had the ability to hit targets in the US from Cuba. This would have put much of the US under threat of nuclear attack. However, this is exactly what happened in the years to come. As the Soviets developed better missile technology, all of the US came under threat of Soviet attack. This threat never became reality, of course, and there is no reason to believe that it would have become reality if JFK had allowed the missiles to stay in Cuba.
The most important impact would probably have been on JFK's legacy. If he had allowed the missiles to stay, he probably would have a much lesser image in the eyes of many Americans today. However, it is likely that there would not have been any serious tangible difference in the way history played out.