Better for what?
Self-defense - Karate is certainly better
Competitions - Depends on the style of karate, some Martial Arts have lots of competitions. If you don't like to compete, find a style that doesn't focus on sport. Gymnastics is much more competitive and is recognized globally. You can compete in the Olympics in Gymnastics, you can't in karate.
Longevity - Most gymnasts don't compete after they hit their early 20's. Then what are you going to do? Many martial artists are still actively participating into their 70's and 80's.
Traditional karate does not require any equipment and can be practiced in a relatively small area. Gymnastics use a variety of equipment types, most of which are not available in the home.
Cost wise, it will depend more on the program and training school as to whether there is any advantage.
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Both are important life skills. Swimming is not only recreational but can also prove to be life saving. Learning karate or any martial art for that matter will enable you to defend yourself in some terrible situation. Both will keep you fit and healthy and exercise all you body muscles.
For some reason I think karate is because you have more skills and they're tricky. Unlikely boxing only has mostly punching and how to do your moves . But they are both great!
It will depend on what your goals are. For self defense, karate is going to be better. For aerobic exercise, swimming is probably better and less likely to injure the joints.