George Bernard Shaw once said: "Democracy substitutes election by the incompetent many incompetent many for appointment by the corrupt few...", and while I don't have nearly such a bleak outlook on our method of government, Mr. Shaw does hold an iota of truth in his quotation. In a perfect world, where everyone is informed, intelligent, and aware of their system of administration, democracy would work perfectly. In a world where there are different personalities, dissimilar concerns and divergent points of view, democracy falls short of the ideal of having all people being equal. Similarly, having a Philosopher-King or an equivalent in control of a country sounds fine on paper, but there would be different philosophies, disputes within the philosopher-king hierarchy itself, and of course, the never-ending task of stabilizing an entire country would daunt even the most qualified person.
It is a mechanical fault of democracy itself, and not the many leaders caught up in a democratic bureaucracy that causes a country to stumble. A democracy is where the government is run by all the people who live under it. To have a true democracy, everyone must vote. People vote to exercise their democratic rights; if only 70% vote, then 70% control 100% of the government. Voting without adequate understanding and choosing candidates for the wrong reasons are symptoms of voting for the sake of voting and not taking an active interest in how our country is run. Instead of making an effort to understand issues and party fundamentals, too many ignorant people actually base their decisions on what the candidates tell them. The result is that everybody feels "burned" by the government, never realizing that they could have tipped the election simply by paying attention. Another problem with democracy is the structure of any government's bureaucracy.
Vote for a party/candidate only in principle, because in practice, they act completely the same. Imagine bureaucracy as a great fast-moving train; even if another engineer takes control, it is incredibly hard to make any large adjustments without severely unstabilizing the train. Similarly, it wouldn't matter if any political party is in power, because any fundamental change would upset a lot of people (one of the unwritten laws of politics: to make a drastic change is to invite political suicide). In the case of a philosopher-king, a lot more could be done because he would have the power of a monarch, yet his judgment would not be watered down through bloodlines (like how decadent the British monarch has become from their stable position of power).
It would appear that the idea of a philosopher king has the best of both worlds: The control of a dictatorship, but the freedom of a (controlled) democracy. (The philosopher king is not defined as concisely as I'd like, so I'm taking some liberties here). Someone who is bred specifically to lead a country would be better than any politician; they would be specialized in the physics of politics, they would have unique insights into old political problems, and could master political double-speak by age 10! No question, a more stable country would develop under a purebred leader, but there could be many more unseen problems that would come along with an absolute ruler. The term, philosopher king would create an image of a monarchical rule, where his word is law. That would have the advantage of streamlining the government, with the absolute leader making quick, summary judgments. Any problems that could develop through a monarchy would not be anything new; more than a few countries have felt (and have rebelled against) the stranglehold of a king holding absolute power over them. Another problem with the philosopher king: which philosophy? A Socrates indoctrinated ruler would have different viewpoints from an existentialist philosopher king. Would people vote for different philosophies as well as their favorite king? There would be as many problems with the mechanics of a philosopher king as there would be with a democracy.
I'm not saying that either is better: Both the philosophy of democracy, and the concept of a philosopher king both sound good in theory, but once the human factor is introduced, an incalculable variable is introduced into any equation, political or otherwise. It may appear that a philosopher king may have a short term upper hand, but eventually, that system will fall under its own bureaucracy; as badly as a system where the ignorance of nation would rule themselves. John Lowell is quoted as saying "Democracy gives everyone the right to be his own oppressor..." so why put more oppression in a country?