Hmmmm... This is a very interesting match, and I have plenty to comment. My conclusion is in the end of this comment, and one thing I should note is that if Yujiro fights out-of-character, he wins this considerably easier.
When comparing the two fighters, it seems that Ryuko should have a massive AP and durability advantage. 8x, as it was stated by people earlier here, and she even has some statistics amplification, becoming stronger the closer she is to death (Which is described as "significant"; I'll consider that as she becoming 50% stronger) and reactive evolution that allows her Kamui to develop more powers the more the fight goes on, and I'll say that, with speed equalized, she is the more agile of the two. However, this isn't as clean-cut as you'd expect. SInce the feat performed by Yujiro, it has been repeatedly stated that he has grown considerably stronger. In fact, in Baki, it's been several years since some of Yujiro's greatest Town-level feats, and it is stated that he improves and gets stronger each day. More than that, Yujiro, when using the Demon Back, can one-hit-kill people who are otherwise mostly unharmed from attacks from his, and tank several attacks that he, in his base form, was very apprehensive to tank (For reference, Yujiro V.S. Kaku Kaioh, arc of the kaiohs). Not only that, but he has several techniques and methods that he uses, even in-character, to considerably reduce pain and the strength of strikes, and also many other techniques that are much stronger than his usual strength that, again, allows him even in base form to wound people that are otherwise almost impervious to his normal attacks. Even Yujiro went out of character, he could use techniques such as the Xiao Lee, that itself allows people to oneshot those that could instakill them otherwise, and become impervious to strikes that would also kill them, and use other styles and techniques that also boost his power. Ryuko's still the stronger one, at least I believe so, but it's not as massive an advantage as previously thought.
Now, skill-wise, I won't even comment. Yujiro outclasses her by a mile. Nothing else to comment. While I very much agree that skill helps more the closer the opponent is to the user's own strength, and less the weaker the user is, Yujiro has the kind of superhuman skill that breaks the bounds of the normal rules. Even if Ryuko was even stronger than the initial supposed margin of 8x, his skill is such that it would still help.
In versatility, there is something interesting. Ryuko has way less versatility and options than Yujiro, the man can incapacitate her in dozens of different ways and has several defensive maneuvers. However, she has two specific capacities that are going to get him in a lot of trouble. Namely, her shockwave creation and regeneration.
To be honest, the regeneration isn't that much of an issue. I do think Yujiro would be surprised enough initially for Ryuko to land a good hit on him, but I don't believe he'd die in that moment, just become much more careful. Perhaps he would notice that right away through instinctive reactions and cellular analysis. That being said, once he knows about it, he can do several things, such as using some inhuman grappling moves, the Benda (incapacitating her through sheer pain; yes, I know she resists pain, but Benda causes so much agonizing pain that even people who can shrug off immense amounts of physical pain with no reaction at all get practically manic and utterly incapable of fighting for several seconds, if not minutes), and some others. He'd also notice her cutting weakness, and really, considering the plethora of "cutting" techniques within Baki, I do not doubt he could do so with utmost skill to cut even more precisely than a scissor.
The shockwaves are a different beast. If Yujiro saw as absolutely necessary, he could use techniques such as the Xiao Lee to combat that, becoming very flexible as to allow the shockwave to pass by him with minimal damage, or to even go with the flow and be launched backwards with it. I do think he could also tank them and merely reduce their impact as much as he could, but it'd be certainly bad for him.
In short, I think Yujiro should win with medium to mid-high difficulty, for the reasons specified above. The thing about Yujiro is that despite him knowing most techniques in Baki universe, at least those that were shown, his method of fighting, when he's serious (Which he would be as he would notice Ryuko's strength right away), is to use "absolute violence"; he uses only the simplest fighting basics (Concepts rather than techniques, like mobility, how to throw punches, dodge, etc.) and uses carefully applied brute force, using the most strength and power he can without sacrificing technique or anything, also applying some of his other powers and using the occasional technique, but mostly relying on himself. If he really went out of character, he'd have this significantly easier. Still not easy, but a lot easier than with his usual methods.
