The "bitness" doesn't matter across the network, and workgroup membership is almost irrelevant in this context too.
I'd suggest you temporarily disable all software firewalls on the two machines in question while you're troubleshooting. Then:
1) Bring up a CMD prompt and test whether you can ping-by-IP in both directions.
2) Same for ping-by-other-machine-name.
If that fails, you've got network-level connectivity issues that have nothing to do with authentication or drive mapping. Otherwise...
3) Can you UNC to a valid share on the other machine? (start | run | \\OtherPCName\ValidShareName
If that fails with an "access denied", try this on the XP box:
NET USE \\VistaName\IPC$
It'll ask you for a password. Obviously, type the password for the Vista account you specified. The response should be "command completed successfully" and you should then be able to browse the admin shares (C$, D$, E$ ...) on the Vista box using UNC syntax (\\VistaName\C$
Otherwise, if you want to map a drive as a specific Vista user:
NET USE * \\VistaName\VistaShare
That tells it to make the connection in a particular user context.