If the "old" box and the new box are member servers, once you restore the shares, you will find that the shares have permissions granted to "unknown accounts". The SIDs for the accounts and groups do not match. Microsoft has released a new (Jan 5, 2000) KB article, Q250267 which details how to copy shares from one member server to another with the ACLS intact.
You use Resource Kit utilities getsid to copy the SIDS from the old server, scopy to copy the files and acls (now Unknown), and Subinacl to apply the getsid data and make it all work. The following command can be used to print out the acls for a file:
subinacl /verbose=1 /file c:\whateverfile.txt /display