There is no causal relation of color vs. any form of compression. You can have millions of colors in a blurry and totally useless image. With regards to JPEG images, simply experiment and compare the results.
Thank you, I began understanding that after you'd mentioned that you can have millions of colors in a blurry, useless image; I see that the same amount of color information can be retained at different image qualities which may make the image be blurry to the point of being not useful or be crisp to the point of being too sharp to be usable.
I've done enough experiments with different qualities of JPEG to figure the differences, and found it convenient to keep saving color-corrected images in DNG format and select JPEG near the final stage of the workflow.
JPEG splits colors RGB into Luminance Y and Chrominance Cb,Cr
(by more accurate nomenclature: inverse gamma-encoded numbers R'G'B').
JPEG compression does not shrink the ranges of Luminance and Chrominance.
JPEG reduces the number of tonal levels in the range, less for Y, more for Cb,Cr,
mainly by reducing higher frequency components.
Best regards --Gernot Hoffmann
Great, that's the sort of thing I wanted to know about.
It makes sense to think that because the ranges of Luminance and Chrominance remain the same, the color information remains the same, but as the the high frequency components are reduced by compression, the file size can be reduced with it.