There are files excluded from the sync, but those should just be system files (so you don't inadvertently break the new server or change its ssh host key). Line 640 in the script is where you can find the default excludes list to see if any of your web server configs would be left out that way. Using "/" (or just hitting enter) when it prompts for the mount point should work as expected and copy all of the server's non-system files.
The IP address will be different on the new server than it was on the old server. Could the web server be configured to bind to the old IP address? You might also make sure the newer server doesn't have iptables set up to block port 80.