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What do you mean by save color and brightness? Handbrake keeps the original levels unless you are converting a 10bit source. Also depending on the player, it can effect the output. I know VLC tends to oversaturate and add a bit of contrast a tad on my Mac vs QuickTime.
If you have a file and use quicktime pro and make changes to color, contrast or brightness, then put it in handbrake to convert to MP4, the new MP4 file does not have any of the adjustments, it reverts the file to original settings.