First, a piece of unsolicited advice: learn how to make your programs work under strictures, as if your career depends on that learning. If you had not commented out "use strict", you would have seen that your "open... or die" statements are using the non-existent var $new.

The core of what you are trying to achieve involves the making a "canonical" version of your data. See the Wikipedia article on Canonicalization for details.

Working, tested code:

use strict;
use warnings;

# See http://en.wikipedia.org/wiki/Canonicalization
sub canonicalize {
    my ($string) = @_;
    
    # Remove everything except certain characters.
    $string =~ tr{A-Za-z0-9 }{}cd;

    # Make case-insensitive (if you want)
#    $string = lc $string;

    return $string;
}

sub match_up_canonically {
    my ( $lines1_aref, $lines2_aref ) = @_;

    my %where;
    $where{ canonicalize($_) } |= 1 for @{ $lines1_aref };
    $where{ canonicalize($_) } |= 2 for @{ $lines2_aref };


    my ( @matches, @nonmatches1, @nonmatches2 );
    for ( @{ $lines1_aref} ) {
        my $n = $where{ canonicalize($_) };
    
        if    ( $n == 3 ) {
            push @matches, $_;
        }
        elsif ( $n == 1 ) {
            push @nonmatches1, $_;
        }
        else {
            die "Can't happen";
        }
    
    }
    for ( @{ $lines2_aref} ) {
        my $n = $where{ canonicalize($_) };
    
        if    ( $n == 3 ) {
            # Do nothing!
            # The matched lines already printed in the @lines1 loop.
    
            # ...or...
            
            # Print the matched lines again, because they may be
            # different, just not different in a way that matters.
#            push @matches, $_;
        }
        elsif ( $n == 2 ) {
            push @nonmatches2, $_;
        }
        else {
            die "Can't happen";
        }
    }
    
    return( \@matches, \@nonmatches1, \@nonmatches2 );
}

my @lines1 = (
    'able baker charlie',
    'roger, fox, dog',
    'Gomez Morticia Cousin-Itt',
    'Wednesday Pugsley Lurch',
);

my @lines2 = (
    'Gomez Morticia Cousin_ITT',
    'roger; fox; dog',
    'Wednesday Pugsley Fester',
    'able baker charlie',
);

my ( $m, $n1, $n2 ) = match_up_canonically( \@lines1, \@lines2 );

print join "\n", 'Matched:',      @{ $m  }, "\n";
print join "\n", 'Non-matched1:', @{ $n1 }, "\n";
print join "\n", 'Non-matched2:', @{ $n2 }, "\n";
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