Both authoritarian and democratic governments have the same tools for controlling and manipulating their economy as long as they are operating within a capitalist economic system. There would be differences in their ability to grow the economy based on how much the government regulates business and what freedoms they allow, but how they're equipped to grow would be the same.
Socialist economic systems have a more challenging task. The government is responsible for the welfare of the population while their people are much less motivated. Whether they produce or not makes little difference in their life.
The answer isn't based on the political system, it's the economic system and the degree of freedom either style of government allows. The problem with authoritarian governments is they're most often about controlling the population, not making them economically viable.