Yep, I have the same problem and can’t figure out what the heck is going on. Here’s the rub for me: If I put that FCP output into iDVD the color and contrast all “comes back” as it where and I have no idea why.
To see a side-by-side example of this, take a look at the following screen shot (URL below). This shows the exported a frame from the FCP clip that I exported to a QT movie (right side of screenshot) and the same frame after the QT movie has been dragged into an iDVD project.
https://www.meeksphoto.com/test/idvd-qtcontrast.jpg
Now, this is no big deal if you’re always going to drag the FCP output into iDVD, but that’s certainly not the case for me; more often than not I’m developing a clip to be viewed using QT and with the washed out colors, well, it’s driving me nuts.