Sadly we know nothing of Barnes' background for comparison, outside of having been a teen U.S. national champ in karate and an alleged "bad boy." We don't know his home school or style or where he came from, family wealth, etc. All we know is he's good enough at karate to clown Daniel in a tournament setting and in impromptu brawls in bonsai shops (this after Daniel had a back-and-forth death match with Chozen the previous summer). But we can infer he's not a complete noob to privilege as Silver puts him up in a fancy hotel and provides a car and driver and a gang of lackeys and Barnes is not only unphased by that, he demands more.
But cardio capacity isn't a material differentiator among teen Daniel, Chozen and Barnes. We never see any of them gas and none of them are big or muscular enough for it to be a likely constraint anyway.
However, all considered if we had to rank them on physical conditioning/toughness (including cardio) as it pertains to karate, I gotta go with Chozen. Even though he's the rich kid (nephew of Sato, the richest dude in town), we're talking rural Okinawa pre-strip mall era as seen in Season 3. So blue collar farming village and Chozen works as a junior manager at a grocery store. He's also the top student of Miyagi Do/Sato Karate (implied to be the most effective karate style in the world) in the literal birthplace of karate. And in S3 we learn that he goes on to become the head sensei of Miyagi Do karate after Sato's death. In the present, he's the only person we've seen clown Daniel in karate, making him arguably the most skilled karate practitioner in Cobra Kai (although we haven't yet seen what present-day Silver and Barnes can do).
On top of that, the man is fucking crazy. In the garden fight scene in KK2, he gives Daniel the spear and invites him to attack, before disarming and beating his ass with his bare hands. After Sato disowns him, he runs into the raging typhoon that levels the entire village and after surviving that, somehow lives off the land alone in the destroyed landscape for days (weeks?) before challenging Daniel to a death match at the festival (when he's almost certainly dehydrated and depleted after that ordeal). Then after losing, he unironically asks to die rather than live as a loser.
So Chozen is twisted, but a hardcore tough as nails MF'er. No one outside of Miyagi (maybe Kreese and Silver in Vietnam) has endured the physical hardship Chozen is implied to in KK2. The bullying Daniel faces is trifling fancyboy stuff by comparison.