Here's the subroutine I came up with. Thanks for everyone who responded. I could never get the flattening the array method to work. It is not very elegant and probably slow, but this is the only solution I could find that prints the right answer:

equal

non equal

equal
[download]

#!/usr/bin/perl
$HASH_SIZE = 100;
%hash1;
%hash2;

for ($i=0; $i < $HASH_SIZE; $i++) {
    $hash1{"i=$i"} = "j=$i";
}

%hash2 = %hash1;

if (&hasheq(\%hash1, \%hash2)) {
  print "\nequal\n";
} else 
{
    print "\nnon equal\n";
}

$hash2{"anotherone"} = "anotherONE";


if (&hasheq(\%hash1, \%hash2)) {
  print "\nequal\n";
} else 
{
    print "\nnon equal\n";
}

$hash1{"anotherone"} = "anotherONE";

if (&hasheq(\%hash1, \%hash2)) {
  print "\nequal\n";
} else 
{
    print "\nnon equal\n";
}


sub hasheq {

    my ($ha1, $ha2) = @_;
    my %h1 = %$ha1;
    my %h2 = %$ha2;

    my @k1 = keys(%h1);
    my @k2 = keys(%h2);
    # do they have the same number of elements?
    if (@k1 != @k2) { 
        return 0; 
    }

    # are the keys the same?
    if ((join '/' , sort @k1 ) ne (join '/' , sort @k2)) { 
        return 0;
    }

    # are the values the same? 
    if ( scalar grep { $h1{$_} ne $h2{$_} } @k1 )
    { 
        return 0;
    }

    return 1;

}
[download]