Gary - I just did a move from a hosted server to my local PC - it took me less than 5 min.
- compressed entire EPESI directory (including modules and /data). Downloaded it, unpacked it (it was about 1 GB in size as it had a lot of files attached in /data directory)
- downloaded a backup of the database (564 kB gz compressed)
- imported the database on my local computer via phpmyadmin (you don't need to unpack it - gz file is fine)
- changed /data/config.php to match database name, user and password
In your case you may have to download all files via FTP if you can not compress the directory on the server.
You may have to edit the config.php file on your computer and upload it if you don't have ability to edit it remotely.
This would be the only difference.
We move EPESI installations between servers, between directories, make cloned copy for testing purposes - all the time. Never had a problem.
My suggestion is to copy EPESI to your local computer first (use Uniserver for example) and see if it works before you move it to another server. This way you will have more control over configuration files, php settings, access to error logs etc.
http://www.uniformserver.com/ - it comes with everything you need: Apache, PHP, MySQL, phpmyadmin