Using unpack, hashes and Test::More:

#!/usr/bin/perl

use 5.026001;
use warnings;
use Test::More;

sub same {
    my ($s1, $s2) = @_;
    my %l1; $l1{$_}++ for unpack "(A)*" => $s1;
    my %l2; $l2{$_}++ for unpack "(A)*" => $s2;
    is_deeply (\%l1, \%l2, "'$s1' ~~~ '$s2'");
    } # same

sub diff {
    my ($s1, $s2) = @_;
    my %l1; $l1{$_}++ for unpack "(A)*" => $s1;
    my %l2; $l2{$_}++ for unpack "(A)*" => $s2;
    isnt ((join "" => map { $_, $l1{$_} } sort keys %l1),
          (join "" => map { $_, $l2{$_} } sort keys %l2),
          "'$s1' ~!~ '$s2'");
    } # diff

same ("ABBABAA", "BAABABA");
diff ("ABBABAA", "BAABBBA");
diff ("ABBABAA", "ABBABaA");
diff ("ABBABAA", "BAABBAA ");
diff ("ABBABAA", "BAABABA ");
diff ("ABBABAA", "BAABABAA");

done_testing;
[download]

-->

$ test.pl
ok 1 - 'ABBABAA' ~~~ 'BAABABA'
ok 2 - 'ABBABAA' ~!~ 'BAABBBA'
ok 3 - 'ABBABAA' ~!~ 'ABBABaA'
ok 4 - 'ABBABAA' ~!~ 'BAABBAA '
ok 5 - 'ABBABAA' ~!~ 'BAABABA '
ok 6 - 'ABBABAA' ~!~ 'BAABABAA'
1..6
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edit: add example for Test2:

use 5.026001;
use warnings;
use Test2::V0;

sub same {
    my ($s1, $s2) = @_;
    my %l1; $l1{$_}++ for unpack "(A)*" => $s1;
    my %l2; $l2{$_}++ for unpack "(A)*" => $s2;
    is (\%l1, \%l2, "'$s1' ~~~ '$s2'");
    } # same

sub diff {
    my ($s1, $s2) = @_;
    my %l1; $l1{$_}++ for unpack "(A)*" => $s1;
    my %l2; $l2{$_}++ for unpack "(A)*" => $s2;
    isnt (\%l1, \%l2, "'$s1' ~!~ '$s2'");      # <- this line is now m
+uch simpler
    } # diff

same ("ABBABAA", "BAABABA");
diff ("ABBABAA", "BAABBBA");
diff ("ABBABAA", "ABBABaA");
diff ("ABBABAA", "BAABBAA ");
diff ("ABBABAA", "BAABABA ");
diff ("ABBABAA", "BAABABAA");

done_testing;
[download]