I would probably :
1) install brand new DA so that you have all of the latest updates, features, and optimal defaults set,
2) make note of all major software versions installed on both systems, such as php, mysql, and webserver and webserver type (in case a site was using an older php version, for example, but is not compatible with a newer php version used on the destination server)
3) run a find /usr/local/directadmin/ -type -d -name "*custom*" on the source server to see if you've setup any custom configurations on the source server you'd like to keep,
4) From the source server:
/usr/local/directadmin/directadmin c
Copy the output to the destination server in a file named old.conf
/usr/local/directadmin/directadmin c > new.conf
diff -yw --suppress-common-lines old.conf new.conf
And see what settings differ to determine if there are any you'd like changed on the new server to match the old
5) (*IF you use CSF*): copy over a copy of the source server's /etc/csf/csf.pignore and /etc/csf/csf.conf files appended with the '.bak' extensions, and then compare them via diff to the new server's files to see if there are any services you've added to your server (e.g., memcached, redis, etc.,) that may need to be installed on the destination server, as well as added to the new server's pignore file or have custom ports opened in the csf.conf.
6) compare all php and apache modules on both servers using comm or diff to ensure that these same modules exist on the destination server so that your sites do not have errors due to missing modules once being copied over
7) use the admin backup/restore system to migrate accounts to the destination server,
8) check all sites on the destination server by editing your hosts file
9) fix any resulting errors
10) update the dns for all sites to load from the destination server
Let us know what issues you encounter!