Yeah, the fight scenes were what honestly allows the entire manga to shine, and makes it so readable. That's also probably the reason the manga and anime bustles from fight scene to fight scene with very little inbetween, because the author knows that's what he's good at and what makes the piece work at all as entertainment, trying to do anything else would have weakened the manga too much and made it mindnumbing to read.
The anime doesn't have these, but the manga has TONS of these little biographies of the characters that give stats and character design background, and all these little comedic 4komas, and all these 'behind-the-scenes' gag strips with the author and his buddies doin' shit; and I just skipped over all of them, they were insufferable. Maybe if I were buying the volumes as a real Japanese person might have when they were first being created, they might have added a little bit of levity at the end of an otherwise bloody and shouty match, but when binging through the entire thing as an American weeb, they were just interrupting and ruining the pacing that the story relies on so much.
But as far as Baki vs Asura goes in fight scenes, it's hard to compare. Asura doesn't give any time to really hype up someone really powerful, it gives so little spotlight to individual characters, while Baki gives tons of time to really emphasize just how goddamn swollen with power and what a shit-brickhouse of muscle somebody is. Asura's characters are definitely exaggeratedly strong, but they aren't half as exaggeratedly strong as Baki characters, which has characters that break physics in their day-to-day life. Asura, in that regard, is a little bit more 'realistic' and so you can actually kinda picture these characters existing and all these competitors in the Annihilation Tournament being closer to being equals to eachother; and in this regard, the fights are harder to predict, because both characters are human and they entered the fight assuming they have a chance of winning; which holds true for the entirety of the show. Baki, in this regard, has far more inequality among it's characters, though in my opinion some of the VERY BEST fights in Baki are emphasized by this inequality, when a "normal" character in Baki (there's no real normal characters in Baki) is pitted against another character who is VASTLY superior to them in every way, and from the very onset the outcome of the fight is predetermined, the weaker character, more likely than not, DOESN'T GIVE A FUCK, because every character in Baki upholds the motto that permeates the entirety of the manga: "If someone is born a male, he will dream of being the strongest man alive. So long as he never gives up this dream, becoming the strongest remains possible." and no character ever gives up on this dream, every character in Baki shares this exact same motivation. Kengan Asura doesn't have a motto like this, some characters do, but most don't; and that holds it back from being a really great shonen battle story.
Also, I would say that Baki is a little bit more inventive with narrative devices than Asura is; where Baki will use (I'd say, sometimes overuse) devices like having a bystander describe the fight after-the-fact; Asura never does, every fight is always a very straightforward affair, though I'd say it uses fake-outs quite a bit too much to build suspense as to who the victor in an exchange is.
Again, Asura is very enjoyable, but none of the fights had extreme impact on me, and I'll likely forget most of them. Baki has fights that I've read and reread and remain in my mind months after the fact. That's how I'm judging it.