I am unsure how to compare arrays of hashes ... -- Lady_Aleena

The comment "Data::Compare does have the facility to compare array references" does not apply with respect to the above doubt. With combination of ...

  # I have not figured out this part yet.
  #    elsif (ref($old) eq 'ARRAY' && ref($new) eq 'ARRAY') {
  #    }
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... it seems you are unsure about comparison of array reference of hash references. (Loose language sinks ships. ;-) Regardless, you would need to loop over array (reference) elements near the beginning of the sub ...

sub deep_data_compare {
  
  my ( $old, $new ) = @_;

  if (ref $old eq 'ARRAY' && ref $new eq 'ARRAY') {

    #  Handle the case of uneven number of elements in
    #  each array reference as you see fit. Here assumption
    #  is that both references have the same number of
    #  elements.
    for my $ix ( 0 .. $#{ $old } ) {

      deep_data_compare( map $_->[ $ix ], $old, $new )
    }
  }

  ...
}
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