Your code is basically correct except that you change the $fname variable by adding the .last extension before it is used to open the a file. So this same value($router.xml.last) is used for both XML::Twig objects, hence you get files that are identical. Try replacing the following:

$fname="$fname.last";
$RoutersLastState->parsefile($fname);
print "Loaded Last State\n";
[download]

with this:

$RoutersLastState->parsefile("$fname.last");
print "Loaded Last State\n";
[download]

Your results will now end up in $router.xml.changes instead of $router.xml.last.changes.

HTH