Give Text::Similarity::Overlaps a try. For example:

#!/usr/bin/perl -l

use strict;
no strict 'refs';
use warnings;
use Text::Similarity::Overlaps;

my( %opt ) = ( 
    verbose => 1,
    Text::Similarity::NORMALIZE => 1,
);

my $mod = Text::Similarity::Overlaps->new( \%opt );
die "$mod failed" unless defined $mod;

my $file1 = 
  "/usr/lib/perl5/5.10.0/i386-linux-thread-multi/Encode.pm";
my $file2 =
  "/usr/lib/perl5/5.10.0/i386-linux-thread-multi/Encode.pm";
  
open $file1, '<', \*STDOUT or die $!;
binmode STDOUT, ":encoding(UTF-8)";

open $file2, '<', \*STDOUT or die $!;
binmode STDOUT, ":encoding(UTF-8)";

my $score = $mod->getSimilarity( $file1, $file2 );
print "The similarity of $file1 and file2 is: $score";

close( $file1 );
close( $file2 );
[download]

It'll take a few minutes, but it comes back with a score. In this case, the result was: 0.999615754082613 for two files exactly the same.

For two completely different files:

#!/usr/bin/perl -l

use strict;
no strict 'refs';

no warnings::anywhere qw(uninitialized);
use Text::Similarity::Overlaps;
use warnings qw(uninitialized);

my( %opt ) = ( 
    verbose => 1,
    Text::Similarity::NORMALIZE => 1,
);

my $mod = Text::Similarity::Overlaps->new( \%opt );
die "$mod failed" unless defined $mod;

my $file1 = 
  "/usr/lib/perl5/5.10.0/i386-linux-thread-multi/Encode.pm";
my $file2 =
  "/usr/local/lib/perl5/site_perl/5.10.0/POE.pm";

  
open $file1, '<', \*STDOUT or die $!;
binmode STDOUT, ":encoding(UTF-8)";

open $file2, '<', \*STDOUT or die $!;
binmode STDOUT, ":encoding(UTF-8)";

my $score = $mod->getSimilarity( $file1, $file2 );
print "The similarity of the two files is: $score";

close( $file1 );
close( $file2 );
[download]

The smilarity score for two completely different files came back at: 0.345969033635878