Does Character B have a severe fear of his own blood or any blood? It’s probably worth remembering, the other guy bleeds too. In terms of weaknesses, fear of blood is probably one of the worst to give a character who participates in any sort of combat. Fighting is incredibly bloody, it doesn’t really matter how flawlessly one fights. Blood is an inevitability, not a possibility. You can cut yourself from getting hit, from falling, from getting scraped on the ground, or from your teeth cutting up the inside of your mouth if that jaw doesn’t stay clenched. Or bite your tongue. (This is why mouthguards are a thing when sparring.)
A fear like that is one which can be fairly easily identified and, once it is, then the other combatant will begin to use it against them. This is especially true if it’s bordering on a phobia, which is what you’re suggesting here. There’s nothing quite like someone realizing “oh hey, you’re afraid of blood” and then either smears some from an open cut across their face or spits some right in the other person’s face.
The real answer to the who would win question is honestly: who is the better fighter of the two. Who is the most adaptable? Who is the most capable of changing their tactics and using their environment? There’s a host of questions that come in on top of “who would win”. It’s not the style that matters, it’s the person who practices it. Style comes with a variety of different skill levels. The traits that most commonly lead to victory are usually observation and adaptability, with the capacity to successfully adapt their available tools (their skills, knowledge, and techniques) rapidly to the new situation.
However, it’s best not to about it from the perspective of “who do I want to win”. This often leads to an unfortunate situation where the writer games the fight. Instead, leave it up in the air and let your characters prove it to you. It’s a sort of doublethink that takes some practice, but it’s worth learning.
One of the most difficult aspects of learning to write fight scenes and combat is realizing that you have to be two separate characters (or more) at the same time. It’s a lot like playing chess against yourself, it becomes very easy to just start thinking about it from the side you want to win. The other important aspect is: you can have all the statistics, but you’ll never really know what will happen until you get into the scene itself. Even as the writer, there may be a lot of factors that you didn’t consider until you really started thinking about it from the character’s perspective or aspects the character notices that you didn’t.
The one with the edge isn’t always the one who wins. (And I’m not particularly inclined to say that Aikido actually has an automatic edge over Kickboxing anyway. I mean, have you seen kickboxers in action? Jesus Christ. Those guys and girls are fast, they have a fantastic sense of balance and timing. Plus, they hit hard. Kicking disciplines can be hard to follow without any experience with them.)
This is me saying, your Beta may be on the right track here.
From a writing standpoint, the inherent difference between kickboxing and aikido is going to be philosophical. In the real world, a lot more is going to come into play, but this is the most important difference of the two worth understanding. Yes, one is technically a “hard” martial art and the other is “soft” but that’s not really the major difference.
1) Kickboxing represents a philosophy of attrition. The fighter comes into the ring with the knowledge and understanding that they are going to get hit, but also that they will use that pain to return the damage tenfold. They’re going to fight and it’s going to hurt, they don’t want to get hurt but they know it’ll happen. They’re going to be more mentally prepared to accept and shrug off the pain. A significant portion of a kickboxer’s training is spent in the sparring arena. It’s possible that Character A will have far more experience facing (and deciphering) the fighting styles of other opponents in a controlled environment. (This is not the same as an uncontrolled environment, but it is worth thinking about.)
2) Aikido. As a Japanese martial art, Aikido comes with a philosophy of “Feast or Famine”. Which is you either perform perfectly or you eat shit and die. Aikido is not Aikijutsu. As a revived martial art, it’s focus is almost entirely defensive and it’s philosophy is pacifistic.(It is a fantastic and fascinating martial art, but is in no way the unbeatable dominator some enthusiasts would have you believe it to be.) It has a great deal of trouble when it comes to moving offensively. Character B ability to fight is dictated by Character A making moves against them or by them being close enough to initiate. If they try to go off their center, then they’ll be at a serious disadvantage. The goal of Aikido though, as a self-defense martial art is to avoid injury, lock up the opponent, prove they are not worth the effort, and allow the practitioner to extricate themselves. It excels on the defensive front. In terms of active aggression? No, not at all. The one thing it isn’t is magic.
Basically, Character B needs to have excellent timing and the ability to quickly get out the way. A good practitioner of Aikido (like many in the videos you were watching) make it look very easy because they are very skilled. Controlling someone else’s body in that fashion is extremely difficult, especially when they know what they’re doing and they don’t want to go.
If Character B can’t get a beat on Character A’s timing, then Character A will start to control the fight. (They will start to do this anyway if they can.) The more you see something, the more one begins to adapt to it. This means Character B needs to remove Character A from the fight fairly quickly. They may start being confused by B with “why can’t I hit them?” but they’ll transition into “okay, so how do I hit them?”. When that happens, A may hang back and start testing B’s defenses with feints in order to get a better read on them.
In terms of training, it’s actually pretty rare for a trained combatant to get more irrational when under pressure or when they’re confused. This is because being irrational and angry leads to more mistakes. It’s best to not mistake “aggressive” for “angry” or “rage driven”. Using anger to fuel you and letting it control you are completely separate, they also lead to different results.
When you frustrate someone, two things happen: they give in to the frustration, get angrier, start making mistakes, and sometimes give up entirely, or, on the other hand, they become more dangerous. Martial training involves the latter. You face a lot of frustration during training, you’ve got to learn to overcome and make it work for you. This will be true of both A and B, though due to different martial philosophies it’ll express itself differently.
Finally, it’s worth remembering when it comes to Aikido and Kickboxing that there are a variety of different styles. This is especially true of kickboxing, which may incorporate variants of kicking techniques depending on what they are training for. A character who trains in kickboxing for self-defense or physical fitness will be a different kind of fighter than one who trains to compete in the ring. Or they could come from a different style like Taekowndo and adapted their kicks to the kickboxing style for the ring. They might even have received some kind of mixed martial arts training. Muay Thai, Savate, Sambo and many others are fairly popular when it comes to bleed over.