Assuming both documents are the same colour space (for example, both RGB or both CMYK), then the other likely cause for the colour shift is the colour profiles assigned to the documents — it's likely they're different.
If you have different colour profiles assigned to each document, Photoshop will either:
- Convert the values of the pixels you're moving between documents (a destructive change).
- Or, the colour values will remain unchanged, but you'll seeing them differently due to the colour profile attached to the documents.
If you're doing RGB icon, interface or web design work, then you should have RGB colour management disabled and should assign documents with “Don't Color Manage This Document“.
This is how you'll want your colour settings set up:
- Working Spaces: RGB set to your display's profile.
- Color Management Policies: RGB turned off.
And for each document:
And, Ensure View → Proof Colors is turned off.
Please note that this advice is for RGB icon, interface or web design work. If you're retouching photos or doing print work, a totally different colour management approach is required (can't stress this enough).
If you'd like more info on why this is, please ask :)