"Power is always dangerous; it attracts the worst and corrupts the best," was Ragnar Lothbrok's saying that ended up describing most of the main characters in Vikings, including his son Ivar. Ragnar's sons were supposed to display their father's intelligence in fighting for power and leading people once they got it. Staying sane while at the top was the biggest test of intelligence in the show, and not all of the sons of Ragnar ed.
Bjorn Ironside did his best to protect his father's legacy, but he underestimated the ambition of those around him, including his mad brother Ivar and ended up dying at his hand, leaving Kattegat with no leader. Ubbe, the smartest of them all, managed to reach the Golden Land, but at what price? On the other hand, Ivar pursued his perceived 'Viking way' of raiding and killing and succeeded at first but it didn't end well for him either. So, which of them was the smartest?
Hvitserk
Hvitserk was the only Lothbrok that didn't achieve anything significant in the show because he preferred to follow rather than take the lead. Lothbroks were intelligent leaders, always looking for the next big challenge and how to make themselves and their people greater. Hvitserk, on the other hand, only followed whoever he thought was the strongest man at the moment, first ing Ubbe before switching to Ivar, then Bjorn, and then Ivar again.
His decision to follow Ivar ruined his legacy as he lost the respect of everyone including the people of Kattegat. He ended up spending the rest of his life struggling with his choices, seeking truth and not finding it, wavering in his convictions, and finally becoming an outcast when he accidentally killed Lagertha. He made so many wrong decisions even when he had the right intentions.
Sigurd
Sigurd Snake-in-the-eye was one of the smarter sons of Ragnar Lothbrok when it comes to emotional and social intelligence. Fans didn't get to see if there was more to his intelligence, though, because Ivar murdered him, but he could have made a great ally for Bjorn Ironside. As a kid, Sigurd was the morality check for Aslaug, reminding her to pay attention to the other kids (including Siggy) and not just Ivar.
Sigurd also exposed Harbard for the liar he was when Aslaug thought he was in love with her. When Ragnar died, Sigurd was the first to propose the formation of the Great Viking Army to avenge his death. He was still encouraging his brothers and the Great Heathen Army to stay together and not follow Ivar when Ivar killed him.
Ivar
"I don't want to follow you, Ivar. You are crazy. You have the mind of a child." Sigurd reminded Ivar just before he killed him. Sigurd was right, Ivar wasn't the best of leaders but he wasn't stupid. He knew that everyone would underestimate him because of his physical differences, so he did everything they didn't expect him to do. Ivar was a very good fighter and a brilliant military strategist. He knew his weakness and turned them into strengths by turning people's sympathy for his condition into .
He also knew how to rally crowds which gave him an upper hand over his level-minded brothers when it came to public . He managed to convince Harald Finehair to him in taking Kattegat from Lagertha by downplaying his true intentions. Even in his lowest moment after losing to Bjorn, he still won from Oleg in Kiev. He played his cards right to get Oleg to help him in his cause of retaking Kattegat, and when it failed, he betrayed Oleg and still bought himself some credit.
However, he was too cruel and struggled to control his emotions, which is why his leadership of Kattegat was so bad. He also led Vikings to their ultimate defeat in Wessex because he underestimated Alfred. He wasn't forward-thinking, either, as he failed to consider that Vikings could not thrive as raiders forever. He missed the bigger picture every time which limited him to smaller achievements that he thought were big.
Ubbe
Ubbe Lothbrok found his golden land in the end, and his intelligence had everything to do with it. Before reaching the Golden land, Bjorn had proved himself as a reliable statesman with his short rule in Kattegat which saw him forge trade alliances his brothers never thought of. During his time in Wessex, Ubbe also proved himself as the best diplomat, securing the lands in East Anglia from Alfred and making friends from the worst of enemies.
Ubbe understood that disagreement doesn't have to mean war, something Ivar never understood. He emerged as the greatest peacemaker of Ragnar Lothbrok's sons, knowing how to deal with people and focus on the bigger picture. He was a great fighter too, but he never picked up an unnecessary battle. He also understood that he didn't have to kill people to prove himself as a strong man which is why he tried to negotiate peace with Aethelwulf after the first battle of York. He managed to avoid a war in England when the three kings, including Frodo, came to raid by choosing to kill one man and save everyone.
He was wrong to trust Kjetill during his trip to Greenland, but he had the best of intentions. His marriage to Torvi was also the best marriage of any son of Ragnar as he took his time to listen to Torvi and found a true partner in her. Ubbe got more things right than any of his brothers.
Bjorn Ironside
Bjorn achieved everything Ragnar hoped to achieve and even more, making him the first true king of all Norway. He was a wise leader, having been taught by the best, from Athelstan to Lagertha. He understood that he had to be the big brother when his father died and managed to keep the family together by winning the of Ubbe, the smartest of Aslaug's sons. When Aslaug was murdered, he managed to prevent a family war by convincing his brothers that killing Lagertha would not help anyone, although he underestimated Ivar's desire for revenge.
Bjorn was also more diplomatic than Ragnar. He didn't have to beg the people of Kattegat to give up Ivar without a fight; he had an army and would have taken the throne. However, he understood that using his army against the people of Kattegat would not make him any better than Ivar. He accepted Harald's coronation as king even when he knew that he was the deserving winner of the crown to prevent a civil war. Bjorn is the one Lothbrok that sacrificed so much for the good of everyone. He made many mistakes with his relationships, but he always made the right decision even when faced with hard choices.