There's no restraints on these techniques. The words needn't be unique in the string nor do they have to be of equal length.

Solution 1: Cancel out common elements.

use List::Util qw/ first /;

my %count;
$count{$_}++ for split /,/, $str1;
$count{$_}-- for split /,/, $str2;

my $different = defined first { $_ } values %count;
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The last line says that they're different if there is any value that is non-zero, i.e. any element not cancelled out.

Solution 2: Use &Test::More::eq_array

require Test::More;
my $equal = Test::More::eq_array(
    [ split ',', $str1 ],
    [ split ',', $str2 ],
);
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ihb