An even faster way is to just zip up your old site on the old site, then log into the new site via SSH and then ftp it from oldserver to newserver, unzip and your there.
This benefits from having the superfast connections at both end of the FTP
Don't have SSH, you can fake it with this small script (save as phpexec.php, and upload it to your server, then run it and use a command line like "cd .. ; zip -r public_html.zip public_html"):
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "
http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="
http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>phpexec</title>
</head>
<body onload="document.form1.cmd.focus();">
<?php echo "Current Directory: " . getcwd() . "<br>"; ?>
<form name="form1" action="phpexec.php" method="post">
<input name="cmd" type="text" size="120" /><br />
<input name="execute" type="submit" /></form>
<?php
if (isset($_POST['cmd']) && $_POST['cmd'] != "") {
$str = shell_exec($_POST['cmd'] . " 2>&1");
echo "cmd = " . $_POST['cmd'] . "<br>";
echo "<pre>output=" . $str . "</pre><br>";
}
?></body>
</html>