This is a question that comes up a lot.
Raw is the unprocessed (or minimally processed) data direct from the sensor. It is just the brightness value for each of the pixels, it is not a color image, but we know which color filter is above each pixel, so we are able to work out the color later. In the computer you take that raw data and convert it into a conventional color video signal defining the gamma curve and colorspace in the computer. This gives you the freedom to choose the gamma and colorspace after the shoot and retains as much of the original sensor information as possible.Of course the captured dynamic and color range is determined by the capabilities of the sensor and we can’t magically get more than the sensor can “see”. The quality of the final image is also dependant on the quality of the debayer process in the computer, but as you have the raw data you can always go back and re-encode the footage with a better quality encoder at a later date. Raw can be compressed or uncompressed. Sony’s 12 bit FS-raw when recorded on an Odyssey or Atomos recorder is normally uncompressed so there are no additional artefacts from compression, but the files are large. The 16 bit raw from a Sony F5 or F55 when recorded on an R5 or R7 is made about 3x smaller through a proprietary algorithm.
ProRes is a conventional compressed color video format. So a ProRes file will already have a pre-determined gamma curve and color space, this is set in the camera through a picture profile, scene file or other similar settings at the time of shooting. The quality of the ProRes file is dependant on the quality of the encoder in the camera or recorder at the time of recording, so there is no way to go back and improve on this or change the gamma/colorspace later. In addition ProRes, like most commonly used codecs is a lossy compressed format, so some (minimal) picture information may be lost in the encoding process and artefacts (again minimal) are added to the image. These cannot easily be removed later, however they should not normally present any serious problems.
It’s important to understand that there are many different types of raw and many different types of ProRes and not all are equal. The FS-raw from the FS5/FS7 is 12 bit linear and 12 bit’s are not really enough for the best possible quality from a 14 stop camera (there are not enough code values so floating point math and/or data rounding has to take place and this effects the shadows and low key areas of the image). You really need 16 bit data for 14 stops of dynamic range with linear raw, so if you are really serious about raw you may want to consider a Sony F5 or F55. ProRes is a pretty decent codec, especially if you use ProResHQ and 10 bit log approaches the quality of 12 bit linear raw but without the huge file sizes. Incidentally there is very little to be gained by going to ProRes 444 when recording the 12 bit raw from an FS5/FS7, you’ll just have bigger files and less record time.
Taking the 12 bit raw from an FS5 and converting it to ProRes in an external recorder has potential problems of it’s own. The quality of the final file will be dependant on the quality of the debayer and encoding process in the recorder, so there may be differences in the end result from different recorders. In addition you have to add a gamma curve at this point so you must be careful to choose the correct gamma curve to minimise concatenation where you add the imperfections of 12 bit linear to the imperfections of the 10 bit encoded file (S-Log2 appears to be the best fit to Sony’s 12 bit linear raw).
Despite the limitations of 12 bit linear, it is normally a noticeable improvement over the FS5’s 8 bit internal UHD recordings, but less of a step up from the 10 bit XAVC that an FS7 can record internally. What it won’t do is allow you to capture anything extra. It won’t improve the dynamic range, won’t give you more color and won’t enhance the low light performance (if anything there will be a slight increase in shadow noise and it may be slightly inferior in under exposed shots). You will have the same dynamic and color range, but recorded with more “bits” (code values to be precise). Linear raw excels at capturing highlight information and what you will find is that compared to log there will be more textures in highlights and brighter parts of your captured scenes. This will become more and more important as HDR screens are better able to show highlights correctly. Current standard dynamic range displays don’t show highlights well, so often the extra highlight data in raw is of little benefit over log. But that’s going to change in the next few years so linear recording with it’s extra highlight information will become more and more important.