This is the sort of question that can never be answered objectively. This is particularly true since the answer, in the United States, at least, is tied in many ways to political opinions about President Ronald Reagan.
There are some historians, mainly those who have a very positive image of Reagan, who argue that pressure from the West was what caused the Soviet Union to collapse. They argue that Reagan, through such actions as his strong support of the Strategic Defense Initiative (SDI), pressured the Soviets to spend more on their military. The same argument is made about the support Reagan gave the mujahedeen in Afghanistan. This argument holds that Soviet military spending broke the Soviet economy and caused the end of the Soviet Union.
There are other historians who argue that there was no massive buildup in defense spending in the Soviet Union. They say that the USSR broke apart because of the pressures of nationalism and because of the poor job that the communist country had done in providing economic prosperity and political rights. In this view, Soviet citizens finally got tired of being poor and having no rights. Mikhail Gorbachev realized this and tried to implement reforms. But the public (and particularly people in the non-Russian republics) were no longer willing to accept communist rule of any sort.
This is something that can never be answered objectively. Each historian has his or her own take on how much each of these factors helped to bring about the fall of the Soviet Union.