A common issue that confuses people who are new to the concept of file permissions and user accounts.
When you access files on the XP system via the Vista system, you are most likely doing so via some limited access account, NOT the account you would use if you were sitting at the XP computer. So, you probably don't have write access to that particular directory. Now, when you try and copy files FROM the XP system, you are doing so under the access rights of the Vista account, where you likely DO have write permissions to the directory.
If you need more of an explanation, then any book covering Windows administration should deal with permissions and user management.
Two computers on my home wireless network. One Desktop (wired to router) running Win VISTA Home Premium the second computer is a Laptop (wireless connection) running WinXP SP3. When I try to copy and past files FROM the VISTA machine to the WinXP SP3 machine I get a message stating I need permission. I am the only user of this machine and I have Administrative Rights.
I have no problem at all copying and pasting FROM the WinXP SP3 machine to the VISTA machine.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic