24 fps doesn't really describe resolution (but then technically neither do pixels...)
Compared to an interlaced-scan camera (50i or 60i), a progressive-scan camera (shooting like at 24P or any other "P" rate) will have improved vertical resolution when doing any film-out or for display on a progressive-scan monitor because the frame is not made up of sequentially-captured fields as in interlaced-scan camera. When there is any movement of the camera or subject, it occupies a different place on each field when shooting in interlaced-scan mode, so when de-interlacing, you get a sawtooth edge to moving objects because one scan line is from one field capture, then the next scan line is from the other field, and then the next is from the previous field, and so on.
But generally resolution of a broadcast video format is described in terms of whether it is standard def (480/60i or 576/50i) or HDTV (720/60P or 1080/60i for example).
But if you're asking if 24P/1080 has more resolution than 60i/1080, again, it's an issue of vertical resolution only IF you plan on recombining the fields for a film-out or progressive-scan display. Either way, it would be 1920 pixels horizontal resolution.
If you're asking if 24P matches film resolution, it's not really the right way to ask the question. First of all, there is 24P standard def and HDTV. And second of all, film includes everything from Super-8 to IMAX.
For theatrical projection on medium-sized screens, HD photography, even though it does not match 35mm resolution, is generally acceptable in resolution (sharpness, detail, whatever.) 35mm negative is closer to 4K (4000 pixels across) compared to HD (1920 pixels across) but you factor in that the printing process in film (or HD-to-film) loses some resolution. So HD that is digitally projected in HD/2K -- thus no loss in resolution from transferring to film and making dupes and then release prints, and then being projected, etc. -- would seem comparable to 35mm print quality in terms of sharpness, if not better.
But in theory, only the new 4K Bayer-filtered cameras like the RED or Dalsa come close to the resolution of 35mm, although a good 4:4:4 3-CCD camera like the Sony F23, or a 35mm-sized RGB-filtered HD camera like the Genesis, also come close (you figure that a 4K Bayer-filtered camera is practically-speaking more like 3K RGB, and a 4:4:4 3-CCD HD camera is nearly 2K RGB, so they are not far off. Also, many 35mm D.I.'s are only done at 2K RGB resolution, bringing film down closer to HD resolution anyway.)
But you're probably thinking smaller & cheaper than all of those cameras...