TL;DR – It depends on what "better" means

Enlightened despotism, as a totalitarian form of governance that seeks to benefit the public, is a difficult topic to judge. As a whole, despotism, of course, is bad. However, democracy, too, can end up with drastically negative effects for swathes of the population—not to mention individuals in other nations who are affected by trade, war, and the other foreign interactions of democratically-formed governments.

There is not a significant array of examples of enlightened despotism throughout history, at least compared to democracy (or just plain despotism). Moreover, enlightened despotism is by and large a thing of the past—occurring primarily in times when democracy had not yet become a widespread, global form of governance—thus, democracy and enlightened despotism are difficult to compare.

If we assume a fully enlightened despotism (a ruler actually improving the lives of all citizens), it is better from a consequentialist point of view; by definition, here, enlightened despotism will be beneficial. If we assume a full democracy (without many of the modern barriers, like gerrymandering and voter suppression), it may be better from a deontological perspective—though may not have overall beneficial effects for the populace. Enlightened despotism may also eliminate the difficulties of bureaucracy within democracy. Regardless, one is only better than the other depending on an individual's personal view of a better society. Some may say the best society is one without poverty, hunger, or other material ills, others may say the best society is one with equal rights and opportunities.

TL;DR - Enlightened Despotism cannot be sustained.

Assuming enlightened despotism is entirely possible, and that the countries in question will respond positively to either form of governance, enlightened despotism is the less ideal option for its inability to last.

Perpetuity is written into the framework of democracy; new representatives and officials are elected as time passes, reflecting not only the shifting ideals of the community but ensuring that governance itself continues.

This is not true for enlightened despotism. In event that the enlightened perishes - either prematurely, or merely upon reaching the end of their life - who remains to take up the mantle? Given one good, enlightened ruler, what guarantee is there for another?

It is necessary for a good government to be able to sustain itself and, while democracy is not always manifest in the most ideal form, its ability to ensure governance exists places it above enlightened despotism. One can also argue that the fluidity inherent in a democratic system ensures that a particularly damaging administration can be replaced and voted out; this is not systematically possible in enlightened despotism.