Ok. I stole a lot of the chipmunk's code (because I'm lazy and didn't want to type...). Instead, I trade speed for memory by using one hash for both old & new.

sub compare_sites {
  my($old, $new) = @_;
  if (-M $new > -M $old) {
    ($old, $new) = ($new, $old);
  }

  open(OLD, $old) or die "Can't open $old: $!\n";
  open(NEW, $new) or die "Can't open $new: $!\n";

  my %hash;
  my $omsk = 1;
  my $nmsk = 2;

  while (<OLD>) {
    chomp;
    $hash{$_} |= $omsk;
  }
  while (<NEW>) {
    chomp;
    $hash{$_} |= $nmsk;
  }
  close(OLD);
  close(NEW);

  for (sort keys %hash) {
    if ($hash{$_} == 1) {
      print "$_ went down overnight.\n";
    }
  }
  for (sort keys %hash) {
    if ($hash{$_} == 2) {
      print "$_ went up overnight.\n";
    }
  }
}

compare_sites("newsite1.txt", "newsite2.txt");
[download]

Now you could just go through the hash once and push into arrays as well, but then we might as well use the chipmunk hash. (Dance or Dish?)