Okay! This may change depending on how the additions I proposed go on...
Just to clarify Brad's power level, even before his second key, he is considerably stronger than the feats displayed on the first one, as he evolves a lot through the game and gets stronger, and the Joy buff is, indeed, a very significant one. If we go by game stats, it multiplies his AP and dura between 2 to 3x.
In any case, this is a promising fight. I really like the concept of both characters, and I feel like their interactions would be interesting, but on the ring of battle, they are going to be tested. I've already come to a conclusion, but breaking down the analysis will help.
In power and durability... I'm unsure who has the advantage. I mean, Baki is quite above 9-A, but so is Brad, and with Joy, he multiplies his own strength, but so does Baki through several of his techniques and abilities. I'm inclined to say that Brad is stronger and tougher, but it might not be the case.
Speed is interesting, I'm pretty sure Brad is faster; the feats that Baki scales to and is quite above to, Brad scales the same way but done much more casually and at much tougher circumstances. Dodging supersonic blows and doing them, and being considerably faster than them? Even at the lowest speeds and before growing more powerful, Brad could dodge several gunshots at very close-range, from several targets at once, and move at similar speeds to bullets. Granted, not easily, but he grew continually faster. In fact, if we take the Hypersonic rating on his profile, he'd have the definite speed edge. However, Baki has many speed amplifying abilities, but more importantly, he is certainly the more agile of the two. With skill, he can further diminish Brad's advantage. So, I think that Brad is the faster one, even with Baki buffing himself, but Baki is the more agile and can minimize a bit the difference through skill.
Skill-wise, Baki is way greater. I love Brad, and I'm the first to defend any notion that he is a very skilled fighter, and arguably, he's better than Baki at taking care of multiple opponents and against weaponry, more in-line with Motobe than Baki in his method of fighting, but on a straight on, unarmed slugfest... Baki is simply too much. Brad is the master and creator of the Armstrong Style of Karate, with experience against multiple unarmed and armed opponents. The greatest skill feats and skill-related powers that Brad has are: 1. Beating champion-class opponents in direct fights. 2. Beating up to five people at the same time, with them not being too much weaker from him physically. 3. Beating up people with decades of experience in fighting. 4. Instantly learning and incorporating skills from martil arts scrolls to his techniques just by reading them.
All of that, Baki has done while vastly younger than the third key, and with greater ease. He can copy techniques and whole styles, and improve upon them, by merely glancing. His skill is precise to milimeter levels, his movements outstrip people that have shown more impressive talent than Brad. I won't say Brad is nothing to Baki, but he is very much less skilled.
Power-wise, versatility and stuff, I see a weird case of Baki's raw skill being the greatest "hax" he can bring to the table, and frankly, the only one he needs. Benda could be very effective, of course, but I don't think he'd use it, he seems rather unwilling to use it under normal circumstances. His other skills and more esoteric abilities can either be resisted or cured through items that Brad does usually carry. Brad really does not bring anything unusual aside from his fire attacks, everything else Baki can deal with just fine. Granted, his fire attacks do grant a range advantage and are quite a boon, but frankly... I don't see them compensating for Baki's sheer skill.
My veredict is that Baki should win with mid-high difficulties. Brad shoud be stronger and more durable, and certainly faster, and the fire attacks are something that I don't think anyone in Baki's universe has ever dealt with. Brad is very pragmatic and willing to use every single item and resource at his disposal to beat Baki, but it shouldn't be enough to match him. Brad isn't one to keep retreating and bombarding Baki, and I doubt he'd even manage to pull it off due to Baki's greater mobility. Once Baki gets close, his skill should allow him to dominate the fight, despite Brad's possible physical advantage.
Note that I'm considering BASE Brad. If this was Mutant/Failure Brad, this gets significantly harder to judge. In fact, Brad might even win, as he'd better resist most stuff on Baki's arsenal and gets a hefty buff to his strength and durability, and makes many of Baki's more haxxy abilities that might rely on control over nerves, pressure points and stuff be rendered very ineffective.
