from the documentation where and with which file format you (optimally) do the "correction". Below is what I can gather from the documentation, don't quote me as I do not have a 5DIII
: Lens aberration correction = corrects Peripheral Illumination (vignetting) and CA (Chromatic Aberration) depending on the lens used. It seems that lens compensation will be applied to the JPEG file while the raw file will remain uncompensated. However...
: RAW image processing = allows you to process Raw-images in-camera and adjust certain parameters (including: Peripheral Illumination, CA, Distortion, and others).
Digital Photo Pro
allows you to correct your raw files for Peripheral Illumination (vignetting), purple fringing (color blur) and CA based on lens profiles. As noted above, this can be done in-camera, but it seems that the (Canon) software gives you more control. I use DPP for my 5DII images and film scans...
From your recent e-mail, I guess you already knew that