Actually, the way you are doing it, you are comparing arrays. Therefore you may find useful this node:

comparing arrays

The best method there was MeowChow's at (MeowChow) Re2: (Efficiently) comparing arrays

To take advantage of hashes capabilities, though, I would rather use something like

#!/usr/bin/perl -w
use strict;

my %first = ( aa => 1, bb => 2, cc => 3, ee => 6);
my %second = ( bb=> 2, cc => 3, dd => 4 );

sub compare_one_hash_keys {
    my ($h1, $h2) = @_;
    return grep ( {not exists $h2->{$_} } keys %$h1)
}

sub compare_both_hash_keys {
    my ($h1, $h2) = @_;
    return grep ( {not exists $h2->{$_} } keys %$h1),
           grep ( {not exists $h1->{$_} } keys %$h2) ;
}

print  compare_one_hash_keys( \%first, \%second), "\n";
print  compare_one_hash_keys( \%second, \%first), "\n";
print  compare_both_hash_keys( \%first, \%second), "\n";

__END__
prints:
aaee
dd
aaeedd
[download]

The first sub returns an array of keys present in one hash and missing in the other one. The second one combines the differences in both hashes. I think you may use this method to implement what is closer to your needs.

 _  _ _  _  
(_|| | |(_|><
 _|