To train to win a fight you need sparing. Full contact sparing in boxing, kickboxing, or even karate has dangers. A practitioner has to work up to full contact sparing in a controlled way. And even then there is risk of brain damage. I'm not up to date with the latest science, but I wouldn't risk my child's brain on something as unimportant as winning a fight.
On the other hand, with grappling sports like wrestling, judo, BJJ, you can start sparing the first class. And the risk of brain injury (I assume) is less than every other contact sport. So your child will get more time sparing. Which would translate to better real life fighting skill.
In the end, by being in some sort of combat sport your child will probably lose interest in winning fights on the street or playground. Every time they show up to class they are defeating others and being defeated. It loses its emotional charge and they don't need to prove themselves to random people.