I found Aikido was good. Focus on defense, and no attacking. Lots of exercise and meditation. I would come home exhausted and sleep like a baby. And actually came in handy twice.

Definitely rock climbing

A air pellet gun to teach them marksmanship and the importance of firearm safety.

If being (more broadly) useful for self-defense would be a desirable factor in making this selection, I add my vote for Judo or Brazilian Jiu Jitsu.

Both of those give the practitioner a lot more options for controlling an attacker without hurting them too much, compared to Karate/TKD. Also vastly less chance of getting a head injury while training or competing.

I'll put in a word for my preferred sport here.

My super energetic boy has been rock climbing since 7.

Strength, flexibility, balance, self confidence, progression is based on solving problems, climbs are graded.

Want to expend energy and stay fit? Gymnastics and tumbling. Especially at 6. The martial arts are a good place to start a self defense track, but a 6 year old has a very hard time understanding the body kinetics they are trying to mimic.

Just pick one, if she doesn't like it try the other, and if she does like it and gets proficient at it, maybe she can try the other later on. Really can't go wrong here. I knew plenty of kids when I was in school who had done multiple combat sports and martial arts over the years.

You can become black belt in most martial arts as young as 15-16 (assuming you have the skills required). I can imagine that kinda achievement being a core childhood memory. 10 years of hardwork being rewarded!

If you can only choose between those two, I would prefer karate, mostly because later in the sporting career tae kwon do becomes excessively violent (to the point of complete knockout and worse) whereas karate remains softer.

But at a young age, the spirit and the style of the dojo are much more important, so try both and then choose the one that has a better feeling.

My son attended a different variety at that age, and we hoped there would be focus on discipline and spirit - but there was none at all, it was just about kicking things. Very bad trainers with no people skills. So we took him out from that again. Turns out swimming was his thing - just had to discover it.

choose whichever, most children go down easily with either.

Edit: i should have read the body of the post

As a generally energetic and hyperactive dude, I'd suggest track, perhaps swimming. My mom got me on both karate and TKD as a kid and, between the dead time and slow and repetitive nature of practicing moves, I was bored, annoyed and not tired out enough. 🤷

Having done both, Tae Kwon Do is almost identical to Shotokan Karate. Karate can also involve weapons, depending on the school.

You just need to remember there are multiple "styles" of Karate much like there are different styles of Kung Fu.

All of them are excellent for fitness, self-confidence and discipline.

You can't go wrong with any of them, to be honest.

I think if she likes the local dojo and teachers is much more important than which discipline you pick. These places usually offer the first session for free or at least let you observe a session. So you should try them out and see which one she likes more.

Either is fine as a discipline, as long as the program is tailored to kids her age. More important is the environment in the specific gym/dojo she goes to. It should be fun, supportive, and not put too much pressure on the kids.

Tae Kwon Do features a lot of high kicking, which can be difficult for young kids that haven't developed their balance yet.

Or maybe it's what she needs to develop her balance. I dunno, kids are like little aliens.

I did Jiaido, Jiu Jitsu and very briefly Aikido. All of them were great, because they created a safe space. Everyone was respectful, cared about consent, it boosted my self esteem and made me feel strong and capable - all good for a girl to learn. I figure as long as this is part of the sport, it doesn't matter what martial art they choose, as long as they enjoy it.

...but Jiu Jitsu was also the most fun xD

Jiu jitsu.

Karate is far better if teaching actual self defense is part of the goal. Tae Kwon Do is very questionable in terms of application outside the sport context. Of course, caveat is that, as with anything, it also very much depends on the skill of the instructor.

Jiu-jitsu or judo both great for kids

I'd recommend Brazilian jiu-jitsu. Useful life long skill, they teach discipline, and belt progressions to keep them motivated.

In my honest amateur opinion karate seems more about both strikes and kicks, while the other one is basically almost all kicks.

Either would be fine I suppose. Also depends what you want to get out of it. Both sports will make a kid tired, both will have some sort of discipline build in.

Why decide now? Try both, see what the kid likes better. At a young age it is mostly about who their friends are and what they are doing anyway.

@WeAreAllOne Taekwondo is a core Olympic sport while Karate has only appeared once, so there's the motivational factor of seeing top level competition being televised.