I was a bit dismissive of Bare Knuckle III when I first played it, the flow of the game being much faster and aggresive compared to 2 caught me by suprise and I couldn't really get use to it very well. After giving it a proper play, I found stuff that I end up liking more that it's predecessor and began to apareciate it on it's own merit; more and faster enemies, a new and more flexible implementation of your desperation attack, and even the weapon pick ups have some more depths to them as they give new moves to the characters, except the Kangoroo, who can't pick them, because he's wearing boxing gloves.
I would like it more than Streets of Rage II by a fair share, but the game has a fascination for throwing worthless gimmick at you, which only become more aggravating in subsequent playthroughs. The loader segment might suprise you the first time you see it, and you'll feel good figuring it out the second, but then you gotta do it a third, fourth, and a million times, without alteration or any actual risk, it becomes a big time sink. Same could be said about the train section with the ninjas, or when rescuing that kidnaped guy, or when you end up fighting a literal claw machine for some reason. I would have preferred if the game focused more on "consider the place you're fighting in" like the level with pits or the first part of the train level, instead or "stop fighting to do this other thing."

Really fun sequel that greatly expands the character mechanics, with dashes, dodges, special inputs that you can cancel your jabs and a super that will help you get rid of the most annoying enemies instantly. Each character has their own secret tech, such as Guy and Lucia's dash attack combos, Haggar's whole grappling play, and Dean's (my favorite) which has a very short throwing range but makes up for it with some strong frame traps to catch enemies in their wake up animation. It's great to master them all, but the game design is a bit lacking; enemies have become faster and always try to attack you from behind like mosquitoes, but they can barely keep up with the player's mechanics. This is most evident during the bosses, some of them don't fight with any grunts (like the final boss lol) so there's nothing stopping you from cornering them into a wall, and even then if you're using one of the slow characters , you only have to be aware of their wake up attack, really.
I still had more fun with this entry than the previous ones, but it's missing that claustrophobic feeling of the first game, where your muscle guy is only slightly stronger than the evil muscle guys you're fighting.