Even if Discord DID lead with it, how strong is his Existence Erasure?
Immortality (Types 1, 3, 7, and 8. Hair Ball users should be capable of living forever and boasting no lifespan, along with being able to lose their whole body, mind, and soul, and still be alive. Bo-bobo has killed the Demon King and everyone in Hell, and can come back from any afterlife. Bo-bobo has been both a vampire and a zombie before,
and his Type 8 is due to being reliant on his Hair Soul, which can survive even if his body, mind, and soul are completely erased)
So, where is Bobobo's Hair Ball (Which holds his Hair Soul) normally, how can Discord know about it, let alone know he needs to get rid of it, & how does he get rid of it?
In any case, their personality clashing is interesting. Bobobo may act ridiculous, but it's as a strategy to confound their opponent into submission.... And the absurdity is stuff Discord would just find it hilarious.
But on the other hand, I don't recall Bobobo laughing, nor showing amusement much, which Discord would find annoying, or a challenge. (Willingness to kill aside.)
Even without that, Bobobo has Resistance to Petrification, Wind Manipulation, Paralysis Inducement, Mind Control, Sealing, Dream Manipulation, Transmutation, & Possession.
Also, Telepathy (Depending on use), Information Analysis & Instinctive Precognition may help. (Although, Instinctive Precognition to predict Discord, the embodiment of Chaos, who's probably naturally unpredictable, might not help as much.) And Probability Manipulation.
Bobobo is a challenge to defeat. The only thing MIGHT be BFR (In part because he only has Interstellar Range, presumably for Teleportation, and Portal Creation is in one of Bobobo's higher keys.) Not sure if Bobobo's Resistance to Sealing is relevant.
If he is killed, Resurrection helps. Cloning might also help if Discord only BFRs one at a time, and he might try that too late.
Both of them have Power Nullification. Both also have Time Travel, but Bobobo is for appearing in a story 1,000 years in the past; He might use it for absurdity, not as a tactic.
Discord's issue seems like he might not try BFR first.
Discord's Intangibility might not help, because of Bobobo's Soul Manipulation, Death Manipulation.
Besides that, Bobobo's Conceptual Manipulation (Which might be too limited to help) is another win condition. Transmutation, too, since, wasn't Discord inactive for a while after being Petrified?
Also, I don't know the exact values they're scaled to (If they're present, but....)
Discord:
Attack Potency: At least
Star level (Defeated both
Celestia and
Luna at once with ease, who themselves can raise the Sun and Moon with immense ease. Is possibly the one responsible for creating his own realm. Said to be able to defeat the whole changeling army with just a sneeze. Stronger than
King Sombra)
Bobobo:
Attack Potency: At least
Large Star level (Is able to hurt the Three Civilizations who could take attacks from Bobopatchnosuke before Majide Time. Moved a background full of stars across the sky when turning it to night time. Funny Sugoroku is a pocket reality made by Bo-bobo that had a background full of stars)
The difference between baseline and maximum
Star Level is ~5.59x and for
Large Star Level, it's ~715.59x .
So, how hard Bobobo smacks Discord (Even if he thinks to go Intangible, he has several forms of Elemental Manipulation, which might work.) depends on how far into their tiers they are.
Conclusion:
Overall, I think Bobobo has slightly more win conditions, resists several of Discord's, has several powers that help him avoid being exposed to Discord's powers or to learn how to fight Discord (which, going by Bobobo's intelligence section, he's actually VERY good at.), & Discord has to resort to one specific one, which he might not do first, since he wouldn't initially know to do so.
Not only that, Discord is often casual, underestimates foes, & would laugh at & enjoy Bobobo's natural strategy of trying to confuse & freak out his opponent; Discord would probably find Bobobo entertaining, likely making him reluctant to end the fight, or willing to prolong it.
But Bobobo would see a challenge, puzzle, or reason to try much harder at Discord, and might just bust out his win conditions sooner, instead of goofing around as much as normal.
I'm voting Bobobo Mid-High Difficulty.