Aside from their cultural origins, each style has significant differences -- karate is more linear, with a preponderance of "striking" moves, while kung fu is more fluid with more "circular" motions. I won't pretend to be an expert on either or to weigh in on the debate over which is better (if, in fact, one is more superior than the other). Both are legitimate martial arts and provide excellent self defense techniques. Practitioners of either combat form can develop discipline, strength, and spiritual benefits.
In movies and television, both styles have been showcased quite well. Most showcase a hybrid of various martial arts styles, more for aesthetics that best suit the filmmakers' fight choreographies rather than sticking to a specific style's strict rules.
Nevertheless, I enjoy martial arts films and TV shows -- Enter the Dragon; Drunken Master; Kung Fu; Crouching Tiger, Hidden Dragon; Kill Bill; and many more, for their visual action elements than for their instructional value about definitive martial arts technique.
Kung fu seems to be more prevalent than karate, but in a world where mixed martial arts are becoming the norm, borrowing from different styles and blending them all into a unified fighting technique that is more about flash than substance,
maybe it might be beneficial for movie makers to acknowledge the unique styles and adhere to their confined parameters.