Was Reagan more responsible then Gorbachev for the end of the Cold War?

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.