You should read the documentation for Array::Compare. It's useful. It's written to answer these sorts of questions. I think you simply want to change $comp->compare to $comp->perm. This is in the module's POD. Here's a test example:

#!/usr/bin/env perl

use strict;
use warnings;

use List::Util qw(shuffle);
use Array::Compare;

my @array1 = shuffle(1..100);
my @array2 = shuffle(@array1);

my $comp = Array::Compare->new;

print "perm:    ",
      $comp->perm(\@array1, \@array2) ? "Same elements\n"
                                      : "Different elements\n";

print "compare: ",
      $comp->compare(\@array1, \@array2) ? "Same elements, same order\
+n"
                                         : "Different elements or diff
+erent order\n";
[download]

The shuffle gives a 1:100! chance of the lists being in the same order, I think. So for this test we can usually assume that the elements start out in dissimilar orders. But we do test for that just to be sure. If we run it the output should be:

perm:    Same elements
compare: Different elements or different order
[download]

So even though the elements come in a different order, the perm() method determines that we got the same elements.