Many leaders and monarchs are judged on their success rather than their intelligence or ability. All of them existed in their own time and had their own difficulties and advantages to deal with. Whitewashing or blackstaining is extremely common as well. Some leaders formed great cults around themselves and had sagas or epics written about themselves and their exploits. At times, these sagas, myths, epics and propaganda have been adapted into our history books.

For example, we herald the stubbornness of Churchill as clear-sightedness and moral fibre, probably because he eventually won, yet the stubbornness of Karl XII of Sweden is usually put forward as a great character flaw that eventually lost him the Swedish Empire.

Karl XI of Sweden was most likely what we would today call dyslectic, had a problem with his speech and were unable to form proper relations with people, leaving his wedding bed to inspect the guard at 05:00 in the morning. Yet his foreign policy, aligning Sweden with the naval powers (England and the Netherlands) and building a powerful army , yet keeping the Kingdom at peace and prosperity means that most remember him as successful and a strong ruler with devotion to work and his duties.

Frederick the Great bankrupted Prussia, getting it into wars with France, Austria, Sweden and Russia at the same time, losing Berlin to a Russian occupying force in the process, and Silesia was the only thing he could show for it. Silesia turned out, 120 years later, to be a prime coal-producing region and the most important industrial area of Germany outside the Ruhr, and Frederick is now remembered as the Great, despite the fact that many would probably not think of him as such had that not been the case.

Gustav Eriksson (Wasa) of Sweden seized private and church property, brutally repressed dissent, crushed revolts, increased taxes and centralised the Kingdom and is fondly remembered as a founding father of Sweden, while Lenin, who did pretty much the same thing in Russia, is remembered as a bloody dictator.

Monarchs are human. They have character flaws. No-one remembers Churchill's focus on secondary or tertiary fronts, or his mistakes with Singapore or mishandling of the situation in North Africa and Greece. His alcoholism is downplayed and his inability to build support for his (essentially correct) opposition to appeasement is forgotten. He is remembered as a great statesman.

However, generally, high nobility and monarchs enjoyed several things that would make them more intelligent than the general population - a superb education.

Karl XII was taught to read and write Swedish, German, Latin and French and later taught himself basic Finnish as well. He had no less than 5 teachers (that only taught him) assigned to him at any given time. He studied mathematics, theology, military strategy and tactics, history and engineering, along with a rigourous physical training regime. This made him better educated than most people in Europe and would probably register him as a genius on the IQ scale compared to a regular peasant.

Hundreds if not thousands of books have been written on the rule of Charlemagne - Carolus Magnus, Charles the Great, first Holy Roman Emperor - and the legacy he left. The formation of modern France, Germany, Italy and other countries of western Europe can be traced back to his accomplishments as warrior-king, he whose name is the very byword for the aspirations of countless nobles, kings and emperors to follow in the middle ages down to the modern era. What other monarch's sword do we know by name?

It's not just prowess in war and skill as military and political leader that forms the legacy of Charles the Great. The first theocratic monarch, not just defender of Christendom against the Saracens, but also as founder of monasteries and monastic schools across western Europe, leading the conversion of the eastern Germanic barbarians to Christianity. But these monasteries were not just places of prayer: no, we know of the Carolingian Renaissance by the massive book collections and output of manuscripts - exegesis, natural philosophy, history, jurisprudence - from the countless scriptoria funded by Charles the Great and lead by his court and chancellery.

And that court! The names of scholars that have come down to us: Alcuin of York, Peter of Pisa, Paul the Deacon, and so many more who transformed the transmission of knowledge, the coin of the economy, the laws which bound the various peoples together, the very letters of writing we use today.

Well, this is Charles the Great. And here is Einhard writing about his friend, his master, his beloved king in Vita Karoli Magni:

He was not merely content with his native tongue but took the trouble to learn foreign languages. He learnt Latin so well that he could speak it as well as his native tongue; but he could understand Greek better than he could speak it [...] For his lessons in grammar he listened to the instruction of Deacon Peter of Pisa, an old man; but for all other subjects Albinus, called Alcuin, also a deacon, was his teacher - a man from Britain, of the Saxon race, and the most learned man of his time. Charles spent much time and labour in learning rhetoric and dialectic,and especially astronomy, from Alcuin. He learnt, too, the art of reckoning, and with close application scrutinized most carefully the course of the stars.

And here Einhard closes his description of the great philosopher-king, envy and model of later Capetians and Ottonians, Bourbons and Hapsburgs, Napoleons and Hitlers:

He tried also to learn to write, and for this purpose used to carry with him and keep under the pillow of his couch tablets and writing-sheets that he might in his spare moments accustom himself to the formation of letters. But he made little advance in this strange task, which was begun too late in life.

The image in my mind of perhaps the most formidable western king and emperor since Rome sleeping with his pencil and paper, learning the alphabet, humanizes him more than anything else you could tell me about him. Human intelligence even in monarchs is relative to your measuring stick.

Source:

Early lives of Charlemagne by Einhard & the Monk of St. Gall, trans. & ed. by Professor A. J. Grant (1922, Chatto & Windus, London)

A good example of this would be King John (r.1199-216). John is sometimes considered one of the worst Britons ever, and often labeled as the worst king (though he is sometimes supplanted by William Rufus). Both contemporary chroniclers and modern historians agree that John was a very intelligent ruler -- W.L. Warren, Nicholas Vincent, Ralph Turner, and J.C. Holt all agree on this point, while the chroniclers label him as morally bankrupt but silver-tongued. He was able to work some wicked deals with the Dutch, the Portuguese, his own nobles, and even Philip Augustus. But diplomatic deals often fail even if deals have already been arranged and England was already in financial trouble because of Richard I, leaving the nobles to grumble and eventually revolt when John tried to use heavy taxes to make up the deficit and defend his royal (and family) holdings. He gets a bad rap, but he acceded to the throne in incredibly difficult circumstances. I would argue that it is due to John's intelligence (and the help of Hubert de Burgh and William Marshal) that things didn't turn into a shitstorm almost immediately.

I would recommend any of the biographies by the authors listed above, especially Ralph Turner's.

Hope this helps a little. Happy reading!