Short answer:
Mac is historicaly 1.8 Gamma and PC’s are 2.2 Gamma. If you color correct at 1.8 and display at 2.2, it will be washed out gray and desaturated.
You need to look at your workflow and make sure your color management is in order. Read up on the “Match Legacy After Effects QuickTime Gamma Adjustments” option in AE’s project settings. While you’re there, read up on color management as well.
Also, QuickTime Animation codec is a disaster for managing gamma. Prior to version 7 it was one way, then another, then they decided to do this, then that…. AHHHHHH!! AE even has a
Try converting it to it’s final destination codec (H.264?) and play that on both systems. See if you have the same problem.
Although not completely relevant, this makes for good reading…
Aperture: Color and gamma settings for print and web