I would want to avoid copying the system and configuration files from the old hard drive to the new. This would make the use of diskcopy undesirable. Diskcopy will, more or less, make an image of the entire drive. (If that's what you do indeed want,then disregard my comment.) Moreover, diskcopy is really intended to make exact copies of floppy disks, not hard disks.
I assume you want to copy only data files and the like. Therefore, the use of xcopy with the proper switches may be what you're looking for.
An example (As run from the destination drive):
xcopy d:\data\*.*/s
The /s switch will copy the directory (data) and all subdirectories - the directory tree - within that directory.
Look at this link for a further explanation of the command which includes a listing of all possible switches:
http://www3.sympatico.ca/rhwatson/dos7/z-xcopy.html
Here's a similar page explaining diskcopy:
http://www3.sympatico.ca/rhwatson/dos7/z-diskcopy.html
MS-DOS Commands:http://www3.sympatico.ca/rhwatson/dos7/
(REMOVE the SPACES that may have snuck into the pasted URLs.)