Here is my best guess at what you mean by closest matched dates. I've assumed all the fields except the date make up the primary key that you want to join on. Also assumed all the dates are on or after 01/01/2000;

#!/usr/bin/perl
# 
use strict;
use warnings;
use Date::Calc qw( Delta_Days );

my %hash=();
input_data(1,'out1.txt');
input_data(2,'out2.txt');
output_data('final.txt');

sub input_data {
  my ($ix,$filename) = @_;
  open FILE1, "<", $filename or die "$filename : $!\n";
  while ( <FILE1> ) {
    chomp $_;
    my ( $key, $le, $date, $company ) = split ',', $_;
    my $pk = join "\t",$key,$le,$company;
    push @{$hash{$pk}[$ix]},fmt_ymd($date);
  }
  close FILE1;
}

sub output_data {
  my $filename = shift;
  open OUTFILE, ">", $filename or die "$filename : $!\n";

  # primary key
  for my $pk (sort keys %hash){
    my ($key,$le,$company) = split "\t",$pk;
    
    # get multiple dates
    my @dates  = @{$hash{$pk}[1]};
    my @rdates = @{$hash{$pk}[2]};
    
    # even up number of dates
    while (@dates < @rdates) {
      push @dates,'1900-01-01';
    }
    while (@rdates < @dates) {
      push @rdates,'1900-01-01';
    }
    
    # print out multiple dates for each key
    for my $date (reverse sort @dates){
    
      # use match sub if more than 1
      if (@rdates > 1){
          @rdates = match($date,@rdates);
      }
      # rdates sorted so best match is first element
      my $rdate = shift @rdates;
      print OUTFILE join ' ',$key,$le,fmt_mdy($date),fmt_mdy($rdate),$
+company,"\n";
    }
  }
  close OUTFILE;
}

# match dates by calc days diff
# and sorting to get least diff
sub match {
  my ($date,@rdates) = @_;
  my @days=();
  # split date into y,m,d
  my @d1 = split /\D/,$date;
  
  # calc diff and store with date
  for my $rdate (@rdates){
    my @d2 = split /\D/,$rdate;
    push @days,[$rdate,abs Delta_Days(@d1,@d2)];
  }
  
  # sort array by days
  @days = sort {$a->[1] <=> $b->[1]} @days;
  
  # extract dates 
  return map {$_->[0]} @days;
}


# change mm/dd/yy to yyyy-mm-dd
sub fmt_ymd {
  my $mdy = shift;
  $mdy =~ s/ //g;
  my ($m,$d,$y) = split /\D/,$mdy;
  if ($y < 99){ $y += 2000 };
  return sprintf "%04d-%02d-%02d",$y,$m,$d;
}

# change yyyy-mm-dd to mm/dd/yy
sub fmt_mdy {
  my $ymd = shift;
  $ymd =~ s/ //g;
  return ' 'x8 if $ymd eq '1900-01-01';
  my ($y,$m,$d) = split /\D/,$ymd;
  $y -= 2000;
  return sprintf "%02d/%02d/%02d",$m,$d, $y;
}
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poj

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