This is completely a matter of opinion.
American conservatives like to argue that Reagan was more important than Gorbachev in ending the Cold War. They argue that Reagan kept pressure on the Soviet Union by building up the military might of the United States. This forced the Soviets to spend heavily on their military. This spending made them unable to give their people a good standard of living and that is what made their system collapse.
American liberals are more likely to give Gorbachev the credit. They argue that the Cold War only ended because Gorbachev came in and instituted the reforms that he instituted. They argue that Gorbachev's desire to reform had nothing to do with Reagan's military build up. Instead, they say, Gorbachev acted because he could see that the Soviet Union's communist system simply did not work.
There is no way to know for sure which of these narratives is correct.