In Bjorn, Ubbe, Ivar, Hvitzerk, and Sigurd are some of the most powerful characters in the series, and each seems to be connected to a particular part of Ragnar's personality. Bjorn and Ubbe are the explorers, Ivar is the tactician and the warmonger, Hvitserk is the questioner of faith... but all five of his sons are also powerful warriors, just like their father.
In the end, though, only two of the five Sons of Ragnar make it through to the end of the series - but is this because they are the best fighters, or simply because they make different decisions that lead to their eventual survival? Of the five, who is the most powerful and capable warrior, and which is the most disappointing son?
Sigurd
While all of Ragnar's sons are capable fighters, Sigurd is definitely the weakest of the five - and seems to be a fairly average Viking fighter, rather than someone who stands out as a Son of Ragnar. This may be in part because he doesn't have a lot of opportunity to actually fight. He's seen training with his brothers in a couple of scenes, but when Bjorn and Hvisterk went out raiding (especially their larger journey to the Mediterranean), Sigurd stayed behind in Kattegat.
Even later, he's really only seen fighting when the brothers head to England to avenge their father's death, and there he appears to be a capable - but uninspired - fighter. He gets through the battle along with the rest of their forces, and has some bloodthirsty plans for King Ecbert, but that's about all the fighting that fans get to see. Perhaps there would have been more time to see him really come into his own, but he dies in the season four finale, 'The Reckoning', when Ivar murders him for insulting his manhood.
Hvitserk
Like Sigurd, Hvitserk never really has a chance to shine as a fighter, especially compared to his incredible brothers. However, he does last a whole lot longer than Sigurd does (perhaps because he and Ivar stuck together), and he manages to live through significantly more battles, which is why he is a better fighter overall. As well as surviving through the same battle as Sigurd (to avenge Ragnar's death), Hvitserk had previously been raiding in the Mediterranean with Bjorn, and built up some of his fighting skills there.
Afterward, he fought through multiple major wars, both with Ivar and against him, and even survived the battles that killed both Bjorn and Ivar in the end. However, Hvitserk doesn't have the kind of incredible skill or physical power that Ivar, Ubbe, and Bjorn have, and his struggles with addiction also count against him as a fighter. When sober, Hvitserk is a capable warrior, but when drunk or on drugs (which is a lot of the time, later in the show) he struggles to function at all, let alone fight.
Ubbe
Ubbe may outlive both Ivar and Bjorn, but that doesn't mean he is a more capable fighter - in many ways,ends the series alive and uncaptured (as Hvitserk was initially presumed captured after Ivar's death on the battlefield, although he then appears to be converting to Christianity voluntarily, as a guest of King Alfred), with a wife that he loves, a future that he is ionate about, and even a child to succeed him.
When he is seen fighting, Ubbe is as capable as his brothers, and often incredibly quick. He appears to be extremely talented when it comes to defensive fighting, and is able to move to protect himself and his family with lightning-fast reflexes, which may be another big part of why he survives to the end. However, while his fighting talents are considerable, and keep him alive throughout, he is more of a protector and defender than someone who fights for the love of it... like Ivar and Bjorn.
Ivar The Boneless
When the boys were young, no one would have expected that Ivar would be one of the most capable fighters in the family (and in the series), given his inability to walk. However, as Ragnar himself said to Ivar, he would be constantly underestimated, and this is something he would be able to use to his advantage - which is advice that Ivar definitely takes to heart. He has some truly impressive physical skill, despite his physical differences. He is shown training with his brothers in the woods, as well as murdering an entire group of men in the night, and when he does fight, he is incredibly fast with the little knives that he prefers (as an axe or sword would be difficult for him to manage).
However, Ivar's true prowess in battle isn't his terrifying skill with knives, but the way his mind works. Out of all the fighters in Vikings, Ivar is definitely one of the most ingenious, capable of devising battle plans that take the advantage, and that use incredible cunning and tricks to get the upper hand. Much the same way as Ragnar himself was able to come up with novel ways to attack, Ivar is a master game player, and becomes a byword for terror as a result.
Bjorn Ironside
No matter how brilliant a tactician Ivar the Boneless was, there's little doubt that Bjorn was a better overall fighter - it's even in his name, as he was dubbed 'Ironside' due to his seeming inability to be killed or harmed in battle. Bjorn is also significantly older and more experienced than his brothers, and survives through more than most of them. He battles his way through some of Ragnar's earlier raids, he is with him in their attempts to take Paris, he explores and raids the Mediterranean and even further, and at every turn, he is able to fight his way through.
He is also physically the most imposing by far (and may even be the physically most powerful character in the entire series), towering over his brothers in height and in strength. He is able to knock men down easily in hand-to-hand combat, and watching him in battle is watching an exercise in swordfighting genius. On top of everything, too, is the simple fact that the man was able to kill a bear in single combat - something none of his brothers would have been able to do.