The DEFINITIVE Primarch combat ranking
Context: I've seen many similar posts that discuss which Primarchs are better fighters or who would win in a fight, but they've all either lacked enough justification or ignored that their justifications had extenuating circumstances which significantly tilted the odds in favor of one Primarch or another. I will try my best to avoid this. If I do use more iffy examples of why one Primarch should be ranked above another, it will only be because no better example (that I know of) exists, and I will take the extenuating circumstances into account. The context of the ranking is of how well a Primarch would do against one of his brothers in a flat battlefield where both are armed with their melee weapons and have not yet been empowered by Chaos. Some whose favorite Primarch would shine better in another location might be upset with this, but I feel that this is the only fair way to gauge their abilities as 1v1 fighters. I'll be covering them each from weakest to strongest and put the TL;DR version at the end.
Lorgar Aurelian: I don't think that this should surprise anyone. Lorgar has failed to achieve even an advantageous position against a fellow Primarch in a 1v1, much less win against one. Against both Corax and Guilliman (the latter of whom he fought after being empowered), he was clearly losing and needed his stronger brothers to save him.
Corvus Corax: In Shadow of The Past, warp-touched Corax defeats demon prince Lorgar quite definitively. The fact that Corax won with a relatively clear head and equal if not inferior boons proves that his earlier victory against Lorgar on Istvaan was not just a result of fatherly rage making him uncharacteristically lethal, though it likely played a part. However, I only put him right above Lorgar because of how definitively he lost to Guilliman in his Primarch novel. In it, Corax had the element of surprise yet failed to successfully ambush Guilliman and was defeated in the duel by a single punch while he was unable to wound Guilliman at all. Yes, Corax was wearing only a ceramite chestplate, but Guilliman had punched him in the chest, so it was a fair blow.
Roboute Guilliman: Guilliman is widely seen as a pretty ordinary Primarch combat-wise, which is why he represents the gatekeeper of the midtiers. Besides Corax and Lorgar, he doesn't have any other real victories against Primarchs. Yes, he killed Omegon, but his doing so is only referenced in a single paragraph from a 2004 White Dwarf article, so I don't think it is all that reliable.
Mortarion: To be honest, I don't have anything that definitively proves Mortarion's combat superiority over Guilliman. However, this pair is one of the few that I don't have a concrete justification for, and I think we can all agree that Mortarion was a better fighter even before his ascension, so I'm comfortable with placing him here.
Fulgrim: While both Fulgrim and Mortarion used Chaos boons to fight their opponents, the level of power used and the result of their use differed. On Istvaan, Fulgrim used the buff from the Laer Blade to turn what would've been a defeat against Ferrus Manus into a victory. In contrast, Mortarion became a Demon Prince, giving him far more warp power, but he only managed to achieve a draw against Jaghatai Khan during the Siege. Based on the fact that Fulgrim was able to achieve much more with much less help, he must be a better unenhanced combatant than Mortarion.
Jaghatai Khan: When the Khan fought unenhanced Mortarion on Prospero, the battle concluded with a draw, though both combatants ended up less bloodied than they would be in their later duel. When Manus fought Fulgrim before he was empowered, however, the Gorgon was about to win, which convinced Fulgrim to give in to the demon in the sword and utilize its magic to turn the tide of battle. Since Manus was winning against an unenhanced foe while the Khan couldn't achieve more than a stalemate, he is ranked higher.
Ferrus Manus: Yes, Manus probably would have defeated Fulgrim had the Laer Blade not come into play, but it wouldn't be a landslide. After all, Fulgrim had also scored some hits, and Manus didn't gain the advantage until near the end of the fight. On the other hand, Dorn was virtually untouched and was winning the whole time when he fought Fulgrim in his normal form atop the Saturnine ramparts. Fulgrim may not have technically "died," but he did admit defeat and suffered more than enough wounds to kill a non-demonic Primarch.
Rogal Dorn: Though it may be controversial, I place Alpharius/Omegon (I'm considering them as equally good combatants) above Dorn in the ranking. In the battle between him and Alpharius, the twin has Dorn well on the defensive (pun not intended) and manages a few minor wounds. However, when he makes the strike that is sure to kill Dorn, an Imperial Fist intervenes to blunt the strength of the blow, allowing Dorn to survive and make a counterstrike that defeats Alpharius instead. While some might argue that in reality, the space marine would've made little difference, I defer to the author's intention, which was clearly that the sacrifice Dorn's son made to save his father was what tilted the scales in the Praetorian's favor. Since this ranking is for a 1v1, however, Dorn would receive no such deus ex machina, and Alpharius would slay him.
Perturabo: Despite my best efforts, I could not find an example of Dorn and Perturabo fighting each other, fighting the same person (unless you consider Perturabo's execution of Fulgrim to be a "fight"), or any other means of legitimate comparison. For this reason, I rank them equally.
Alpharius/Omegon: Similar to how I used Manus and Dorn's success at fighting Fulgrim to compare the two, I consider Konrad Curze to be superior to Alpharius/Omegon because of his superior skill at besting Dorn. Yes, Curze probably started the fight in The Dark King with a surprise "sucker slash," but Dorn was armored and could therefore have safely taken an unexpected hit or two before reacting. The fact that Curze was able to leave him in a near-death state despite this and before help had even arrived speaks to his lethality in a way that Alpharius' near-victory could never have.
Konrad Curze: Similar to my comparison of Guilliman and Mortarion, I can't give a single example to definitively show why pre-Chaos Horus Lupercal is a superior fighter to Curze, but it's quite obvious to anyone who has read about the two that he is. Also, Curze acts as a gatekeeper for the toptier ranks.
Horus Lupercal: Explaining why Horus is below Leman Russ is quite easy: The Chaos-blessed Warmaster was nearly killed by Russ and would've died if Russ' emotions hadn't gotten in the way and made him hesitate before enacting the killing blow. Based on that, taking on regular Horus without such hesitation would be a piece of cake.
Leman Russ: Just as with Dorn and Perturabo, the fight between the Lion and Russ during the Dulan campaign shows that the two Primarchs are equally competent combatants, so I ranked them as such.
Lion El'Johnson: Both the Lion and Vulkan have fought Konrad Curze, though in different contexts. In his final battle with Curze on Macragge, the Lion won while fully prepared. In contrast, Vulkan brought an armored Curze to the brink of death on the Night Lords flagship with no armor himself and after suffering from malnutrition and psychological/physical torture. Because of how Vulkan was able to achieve the same result despite many disadvantages, I rate him higher.
Vulkan: The strongest Chaos-free brother Vulkan has defeated is Curze, who is 3-4 ranks below him, whereas the strongest warp-free brother Angron has defeated (while Chaos-free himself) is Russ, who is right below Vulkan. Since Angron has shown greater feats of Primarch on Primarch combat competency, he would be more likely to beat Vulkan in a hypothetical duel.
Angron: During the Siege of Terra, Demon Prince Angron was definitively defeated by regular old Sanguinius, making it clear that he is the superior combatant.
Sanguinius: This will probably be the most controversial ranking decision of all, but I put Magnus The Red above Sanguinius. While yes, he gets beaten by both Vulkan and Russ, they used crutches to do so (3 different deus ex machinas and the Sisters of Silence, respectively). More importantly, authors significantly nerf Magnus when he fights other Primarchs because "Magnus threw a battleship at his brother and they died," isn't an engaging story. However, a hypothetical duel has no obligation towards narrative quality, so he would be allowed to use all the devastating abilities depicted in books where he doesn't fight other Primarchs. As powerful as Sanguinius is, he wouldn’t stand a chance against an unbound Magnus.
TL;DR:
Magnus The Red
Sanguinius
Angron
Vulkan
Leman Russ/Lion El'Johnson
Horus Lupercal
Konrad Curze
Alpharius/Omegon
Rogal Dorn/Perturabo
Ferrus Manus
Jaghatai Khan
Fulgrim
Mortarion
Roboute Guilliman
Corvus Corax
Lorgar Aurelian