Here is my crack at it:

use strict;
use warnings;

#my $ha = [[1,2], [5,5,5], [1,2], [3,4]];
#my $hb = [[4,3], [1,2], [2,1], [5,5,5]];

my $ha = [ [1,2], [5,5,5], [1,2], [3,4] ];
my $hb = [ [1,3], [5,5,5], [1,2], [2,4] ];

if (cmpAoA($ha,$hb)) { 
  print "THEY ARE THE SAME\n"; 
}
else { 
  print "THEY ARE THE DIFFERENT\n"; 
}

sub cmpAoA {
  my @AoA = @_;
  
  return 0 if @{$AoA[0]} != @{$AoA[1]};

  my %hash; 
  foreach ( @{$AoA[0]} ) { $hash{ stringify($_) }++; }
  foreach ( @{$AoA[1]} ) { $hash{ stringify($_) }--; }
  return 0 == grep { $_ } values %hash;
}

sub stringify {
 return "[" . 
   join(",", 
      map{qq("$_")} 
      sort { $a <=> $b } @$_  
   ). "]"; 
};
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-enlil