It is hard to argue that the Depression was anything but a failure of "American style capitalism." It must be said, though, that the Depression was not caused only by capitalism. There were also ways in which the government was involved.
Historians tend to argue that the Depression was caused largely by problems of unfettered capitalism. They say it was caused by things like overproduction by industry and by the huge inequalities in wealth that existed in the 1920s. However, government actions also mattered. Perhaps the most important example of this was the Smoot-Hawley Tariff, which helped make the Depression worse by reducing the amount of trade between the US and other countries.