24 fps is the speed of sound film. Showing material shot at 24 fps on an electronic system that runs at 25 fps (Europe) or 30 fps (US) because of the electrical power system in use (50 hz vs. 60 hz) requires a compromise. Film transferred to PAL video is simply sped up slightly and projected at 25 fps. (Which speeds up motion and distorts the pitch out sound.) Converting 24 fps film to 30 fps video is more complicated. (Google "3:2 pull-down" if you want the technical details.) Obviously you are better off if you can simply display 24 fps source material at 24 fps than if have to convert it to some other frame rate.
It isn't a matter of "faster" or "slower" being inherently better. (In fact, provided you display material at the same frame rate you recorded it at, there is very little difference between watching 24 fps and 30 fps. 10 seconds of film shot at 24 fps takes exactly as long to watch as 10 seconds of HD video shot at 30 fps.)
As far as reproduction goes, it's simply a matter of accuracy. Material shot at 24 frames per second is best reproduced at that rate or some even multiple of it, such as 48 or 72. Film is almost always shot at this rate, & material shot with video cameras for transfer to film, e.g. for theatrical films, will be as well. Some people prefer to shoot video at 24fps, even when the application does not require it, in order to get the "film look". I have even encountered shooting modes which artificially give video the motion-judder produced by 24-to-30 conversion! People in the cinema world have been known to complain that 30 fps is too realistic — it is a property of the eye that, while 30 fps shooting reproduces motion with slightly better accuracy than 24 fps (considerably better accuracy than 24 fps converted to 30 fps by 3-2 pulldown), the illusion of reality is much stronger. Douglas Trumbull's "Show-Scan" system, which ran film at 60 fps, produced such a strong illusion of reality that it made people nauseated, & as a result (also because of the cost) was relegated to amusement-park rides. People with a cinema background often also prefer to work in the more limited colorspace provided by film, because the more realistic colours of video look "cheap" to them. This comes from decades of looking down on television as a "commercial" medium & its users as "technicians" (or, latterly, amateurs), not to be compared to the "artistic" medium of film. I hope such prejudices will soon die out.