I'm assuming you've setup a share on Vista that you are accessing in XP.
In Vista, make the share accessible to everyone anonymously:
- Right-click the folder you're sharing, and click Properties.
- Click the Sharing tab, then Advanced Sharing
- Click Permissions.
- Click Add.
- Under "Enter the object names to select", type "Everyone" (without quotes).
- Click OK.
- Select Everyone in the "Group or user names" box.
- Under "Permissions for Everyone", check the Allow box for Full Control.
- Click OK three times.
You should probably map that share as a network drive on your XP computer.
That should work.
EDIT: I have tested this with the exact same conditions you described, and it worked.