Dictatorships are efficient, in tat there is little to no opposition to major policies or legislation. Thee is no opposition, no long, drawn out debate or campaigns, and dissent is stifled. The media is usually controlled by the state, therefore there is usually little chance for revolution as long as the economy is good and/or the military stays loyal.
Dictatorships in general have vry low crime, as the above poster suggests, that is, they value order over freedom, and many people in a society appreciate and respect that. Mussolini "made the trains run on time". Hitler ended social and political strife in German cities. There are even some older Russians who are nostalgic for the Soviet era under Josef Stalin, because there was less uncertainty and chaos under the old system, or so it seemed.
The major strength of a dictatorship is that it can change its ways immediately, without any of the sort of conflict that occurs in a democratic country when change is needed. This means that dictatorships can be much better at reacting to problems. (Of course, the dictator needs to be really good at seeing problems and knowing the right solutions for this to work out well.)
For example, when Stalin became dictator of the Soviet Union, he was able to remake their entire economy in a relatively short period of time. He was able to order them to industrialize and was able to force people to go work in the new factories and such. In a free society, this would not be possible.
As another example, Lee Kuan Yew was able to make Singapore into a prosperous nation where there is little tolerance for any kind of disorder. Crime rates are extremely low, in part because of the harsh punishments that can be dealt out for what seem to us like minor offenses. This would be less possible in a democracy.
This is not to say dictatorships are good. There are many weaknesses to this form of government, but these are things that could be seen as strengths.