RoboCopy (built in to Windows) is your friend here.
robocopy [path to old server directory] [path to new server directory] /mir /l
/mir
indicates that you want to mirror the old server's directory into the new server's directory
/l
just lists the files that would be copied, without actually copying them
If the number of files and directories is large, you may want to log the output to a file for easier viewing.
/log:C:\logfile.txt
Robocopy will report any files or directories on the old server but not on the new server as New File or New Dir. Files on the new server that are not on the old server will be reported as Extra.
As always, you can run robocopy /?
for additional options.