The martial arts choreographer for Karate Kid was Pat Johnson, who learned Tang Soo Do in the Army. After leaving the Army, Pat met Chuck Norris, and eventually formed an association with Norris, which later became the UFAF.
In the mid 80s, Johnson split from the UFAF. This was around the time Norris met the Gracies. I wonder if Chuck learning jiu jitsu had something to do with that, but that is just me speculating.
Jiu jitsu is good, undeniable. MMA has shown that karate has it's place as well, from Machidas traditional karate style, to Wonderboy Thomson's more modern style. Hell, Paul Felder got his start in Tae Kwon Do, and later got into muay Thai.
I hate style vs style bs. If you choose to limit yourself on the ways you're going to fight, I really feel for you. To me, martial arts is about being able to fight, unarmed and armed. This includes gun-fu. In places without guns, you'll have bludgeons and edged weapons.
Have to know how to deescalate as well, and maintain distance, so if you have to "pull the trigger" so to speak, you have the gift of time.
But yeah, style vs style is bs. Unless it's that Yellow Bamboo shit. That is worthless lol