The direct answer to this question would depend on a definition of what "works" is.
Indeed, unfree societies have more power to voluntarily direct their efforts toward solving a certain goal. We can't deny that slavery was able to build The Great Pyramids. More recent example, totalitarian Communist regime has managed to launch the first human to the space.
Most obviously, the goals are usually chosen so that it made an impression of social prosperity. However, the day-by-day life is often miserable.
Even more than that, unfree regimes are often combined with limited access to information from abroad, so its citizens sincerely think that they are living better than others.
I was born in times when my country has been occupied by the Soviet Russia. My parents were really sure that their salary ($20 per month) was pretty fine. Here's one more example:
This paper says:
Dear komrade [name],
Taking into account the available supplies, you hereby receive a right to purchase in local stores one pair of men's boots available for sale during 1990-1993.
Upon purchase, this invitation is revoked by the store.
So here's the answer: if we define "Dictatorship works" by only taking in account the "great accomplishments", that would be the case, by this definition. However, looking for a "big picture", most dictatorship regimes throw its people into starvation and mostly miserable existence.
It should be said that Democracy is not a magic solution for prosperity. The only meaning of Democracy is freedom. The free economy stands for ability for citizens to feed themselves up, without major external assistance.
Considering this, it becomes easy to answer what's best for India or another developing country. If the people are keen to work, produce some surplus, and manage of the results of their own work, they need Democracy.
OTOH, if the majority of them rather wish to have someone who's supposed to feed them up for free, they need a Dictatorship.