In all fairness, Pope John Paul II made the greater contribution. He reached out in a way that Reagan could not possibly do, and made the fall of Communism peaceful. In fact, Poland could and would become free without Lech Walesa and Solidarity, but without Karol Wojtola (his birth name), none of this would have been possible. The Cold War would have eventually ended, but not as hastily and not without much bloodshed. Poland was heavily entrenched in Communism when he became Pope, and his ascendancy became the hope of the Polish people that they had made it in the world, and that freedom was their birthright. He also tightly balanced the goal of freedom with preventing outright revolt against the communist government, which would precipitate a soviet invasion. Because their previous cultural, military and political leadership (which was ethnic Lithuanian predominately anyway) was wiped out in the Katyn massacre, it took the Pope (who inspired Walesa) to set the liberation of Poland in motion. He was not only the Holy Father of the Catholic Church, but he truly was the Father of modern democratic Poland.
Nice sketch of the Pope's influence in Poland and the cascade of events behind the Iron Curtain.
One guest on Fox News interviewed by Jim Angle, addressed this story, but he was not allowed enough time to really make his point. I believe that he was an ambassador, (current or former, I don't know), from Poland. His name sounded like Brezhinsky but had a lot more letters in it.