(Disclaimer: some of what is written here is taken from my Shonen Hero proposal for both Denji and Power).
What's the Work?
Chainsaw Man is a manga series created by Tatsumi Fujimoto in late 2018. It is pubilished in the magazine Weekly Shonen Jump.
Who are the Characters?
Aki Hayakawa is a major character from Chainsaw Man, serving as one of the two deuteragonists for Part 1.
Katana Man is a character from Chainsaw Man, initially appearing as a minor antagonist in Part 1, and as a major ally in Part 2.
What Makes Them Shonen Rivals?
Aki
Heroic: As a member of the Security Bureau, Aki has protected Tokyo from several devil threats.
Honorable: Aki is typically very polite, and becomes very protective of Denji and Power as the story progresses to the point he's willing to give up his goal of killing the Gun Devil so both of them could live safely, and was also willing to give up two months of his life to save the Angel Devil despite his own hatred towards devils.
Tragic: Aki's family was killed by the Gun Devil when he was a child, leaving him to grow up alone filled with rage for devils.
Intelligent: In sharp contrast to Denji, Aki is a very intelligent and mature man.
Pursues a Big-End Goal: Aki seeks to avenge his family by killing the Gun Devil.
Cynical: He has a hard time trusting on anyone, especially when it comes to devils.
Pessimistic: Aki has a very nihilistic outlook in life, and doesn't see it in a positive light.
Perpetual Frowner: He hardly ever smiles, and is typically sporting a serious look in his face everytime he appears.
Celibate: Due to being a workaholic and being too focused on his goal, Aki hardly shows any interest in romance.
Is a Blood Knight: Thanks to his own hatred towards devils, Aki has no qualms about killing them and even tends to enjoy the task.
Katana Man
Anti-Heroic/Anti-Villainous: After being initially an antagonist, he eventually joins the Security Bureau (albeit for his own greedy reasons), and was willing to help Asa and Yoru to rescue and protect Denji, but only because he wants to kill him himself.
Honorable: Shockingly, even him ends up feeling sympathy for Denji after his reaction to seeing his appartment burnt down in the ground and Nayuta's disappearance, and even makes his own suggestion to cheer him up.
Naturally Talented: Unlike Denji who initially struggled with his Chainsaw Man form, Katana Man is naturally very skilled with his blades, something he even mocks Denji for.
Arrogant/Jerkish: Both would be a massive understatement for him. Katana Man is very prideful of his own strength, and is typically a mysogynistic asshole that is very unpleasant to be around.
Pursues a Big-End Goal: Kill the Chainsaw Man and make him apologize for killing his grandfather.
Believes in the Power of Individual Strength: As mentioned above, he's extremely prideful of his own strength.
Redemption Arc: Somewhat... While he doesn't become a full-on hero he does join the Security Bureau and becomes an ally to Asa, Yoru and Denji (although a VERY flimsy one).
Is A Serious Threat/Villain: Initially introduced as an antagonist that is part of the Gun Devil cult, driven entirely by his wish of killing the Chainsaw Man and avenging his grandfather.
Short-Tempered: Gets angered very easily when things don't go his way.
Born Into Privilege: Katana Man was born as part of the Yakuza, as a result he ended up having a very privileged life, and unlike Denji, he has a very positive opinion about the Yakuza, even going as far as calling them "true heroes".
Is a Blood Knight: He loves fighting so he can brag about his own strength.
Veredict?
Weak yes for Aki, as even though he fits the criteria he was only a rival to Denji in the beginning of the story, meaning he was a rival for a very brief time. Katana Man though is a shocking yes, he's a much more clear rival than Aki that ends up being a perfect foil to Denji, and even though he's VERY unlikable and initially starts as a Hate Sink (which would immediately disqualify him), his appearance in Part 2 ends up toning up his comedic moments such as his pompousness, his over-the-top hatred towards Denji and his dynamic with the Nail Fiend, allowing him to rise to Entertainingly Detestable status, which allows him to qualify.