I would do it like this:
1) Install the same ISPConfig version on both servers.
2) Move all data from the old database to the new database except of the following tables:
alls tables that start with dns_
3) Move the config files and system users from /etc/passwd, /etc/group and /etc/shadow to the new server, not the complete files, just the lines created by ISPConfig.
4) Move the complete web root directory (/var/www) to the new server.
You will find additional posts on thsi topic when you search for "move ispconfig" in the forum.