use strict;
use warnings;

my @lines1 = (
    'The, slow, lazy, brown and green dog',
    qq~I now want it to ignore special characters such as (), ",", ', 
+" etc.~,
    qq~I have code which finds duplicates in 2 text files~,
    );
my @lines2 = (
    'The slow lazy brown and green dog',
    qq~I now want it to ignore special characters such as (), ",", ', 
+" etc.~,
    qq~I have code which finds duplicates in 2 files and spits into 3 
+files~,
    );
my %where;

@lines1 = map {(my $clean = $_) =~ s/[^\s\w]//g; [$_, $clean]} @lines1
+;
@lines2 = map {(my $clean = $_) =~ s/[^\s\w]//g; [$_, $clean]} @lines2
+;

$where{$_->[1]} = ["1", $_->[0]] for @lines1;
$where{$_->[1]} = [($where{$_->[1]}[0] .= "2"), $_->[0]] for @lines2;

for (sort keys %where) {
    my $where = $where{$_}->[0];
    my $what = $where{$_}->[1];
    
    if ($where =~ /12/) {
        print "12: $what\n";

    } elsif ($where =~ /1/) {
        print "1: $what\n";

    } else {
        print "2: $what\n";
    }
}
[download]

Prints:

2: I have code which finds duplicates in 2 files and spits into 3 file
+s
1: I have code which finds duplicates in 2 text files
12: I now want it to ignore special characters such as (), ",", ', " e
+tc.
12: The slow lazy brown and green dog
[download]

is close, but only shows one variant of the dog line. It's really a question of how you actually want to handle that situation.