It is not possible to know the answer to this for sure, but it is likely that democracies are more efficient in some ways and dictatorships are more efficient in others.
It is certainly the case that dictatorships are more efficient in making specific laws. If a dictator wants a law passed, that law will be passed. The dictator is also more likely to be able to get their policies enacted and enforced. It is not likely that bureaucrats will resist the dictator’s will to any great degree. Thus, a dictatorship is more efficient in this sense. In a dictatorship, we would not have the problem that we now have in the US where we clearly need entitlement reform but cannot get it because Congress cannot come to an agreement.
However, democracies are likely to be more efficient at really getting good results. Whenever there is a government initiative that really requires people to get behind it, a democracy is more likely to succeed. In a democracy, people get to feel as if they have some say in government. They do not feel like they are simply being told what to do. Therefore, they are more likely to work hard to implement what a government wants done.
One way to think about this is to think about the difference between slaves and free workers. It may be easier to get slaves (people in a dictatorship) to acquiesce and to do the basics of what the master wants. But only free workers (people in a democracy) will work hard and actually do their best.