What you have to check, is that both PSD files are in the same color space. This will be indicated in the title bar of each image indicating a color space mismatch with an asterisk (*) or that there is no color profile assigned to one of the images as indicated by a pound sign (#). That would account for differences because as you bring a layer in from one color space, you will see it in a new color space.
If the color spaces are different, you can can convert the source image to the color space of the destination image temporarily, and then drag your layer over – Image|Mode|Convert…
Another thing to check is whether they are both RGB images, also indicated in title bar. For example, one image may say "RGB" and the other might say "CMYK". This would also account for color differences, but is not so easily fixed. You can temporarily convert a CMYK image to RGB (Image|Mode|RGB), but it may not produce the correct/desired color.
So without knowing more about your images, it’s hard to say what you’ll have to do to fix them – but the first thing to check is whether they have the same color profile or whether they are the same Mode (RGB v. CMYK).
Peace,
Tony
