Karate and Kickboxing both utilise the arms and the legs so the training requirement in that respect should be equal, but as many styles of karate have 'forms' or 'Kata's' to learn that part of the session will have a much lower impact. As kickboxing lessons usually soley consist of a warm up, kick and punching techniques, bag/ padwork or sparring with conditioning exercises and stretching the intensity levels remains pretty high throughout the class. Though obviously all classes in any style will vary according to the instructors teaching style and lesson content and this will affect the practitioners overall fitness level..
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The fitness level are about level,the kickboxer may have more power due to the more punching capabilities.Karake may have more agility.
Any and all training will result and better fitness. It simply a case of being more active.