Okie, I learned a little bit from critique and here are my first improvements. (Created account name too).

#! /usr/bin/perl -w
######################################################################
+##
# File   :  Perl Schwartzian Transform Demo.pl
# History:  16-Mar-2015 Laszlo first version.
#            19-Mar-2015 Laszlo, improved a little bit.
######################################################################
+##
# A script to demonstrate and measure the Schwartzian Transform.
######################################################################
+##
# Some form of documentation:
# http://www.perlmonks.org/?node_id=1120222

use warnings;
use strict;
use Time::HiRes;

my $maxNumberValue = 100;
my $intSampleSize = 32000;
my @unsortedIntArray = map { int(rand($maxNumberValue)) } ( 1..$intSam
+pleSize );

my $compareAsNumberFunction = sub { return $_[0] <=> $_[1]; };
my $compareAsStringFunction = sub { return $_[0] cmp $_[1]; };

my $noTransformFunction = sub { return shift; };
my $sleepyNoTransformFunction = sub { Time::HiRes::usleep(1); return s
+hift; };
my $returnLengthFunction = sub { return length(shift); };

schwartzianSortVsRegularSort(\@unsortedIntArray, $compareAsNumberFunct
+ion, $noTransformFunction);
schwartzianSortVsRegularSort(\@unsortedIntArray, $compareAsStringFunct
+ion, $noTransformFunction);
schwartzianSortVsRegularSort(\@unsortedIntArray, $compareAsNumberFunct
+ion, $sleepyNoTransformFunction);

my @chars = ("A".."Z", "a".."z");
my $maxStringLength = 300;
my $stringSampleSize = 32000;
my @unsortedStringArray = map { (sub { my $string; $string .= $chars[r
+and @chars] for 1..(int(rand($maxStringLength)) + 1); return $string;
+})->();  } ( 1..$stringSampleSize );

schwartzianSortVsRegularSort(\@unsortedStringArray, $compareAsStringFu
+nction, $noTransformFunction);
schwartzianSortVsRegularSort(\@unsortedStringArray, , $compareAsNumber
+Function, $returnLengthFunction);

sub schwartzianSortVsRegularSort
{
    my @unsortedArray_in = @{$_[0]};    
    my $compareFunction_in = $_[1];
    my $transform4Sort_in = $_[2];
    
    print "Collection of size: " . +@unsortedArray_in . " \n";
    
    # Schwartzian sort, Schwartzian sort, Schwartzian sort, Schwartzia
+n sort, Schwartzian sort
    ##################################################################
+########################
    my $schwartzianStart = Time::HiRes::time;
    my @schwartzianSorted = map  { $_->[0] }
                 sort { $compareFunction_in->($a->[1], $b->[1]) }
                 map  { [$_, $transform4Sort_in->($_)] }
                 @unsortedArray_in;
    my $schwartzianDuration = Time::HiRes::time - $schwartzianStart;

    # Regular sort, Regular sort, Regular sort, Regular sort, Regular 
+sort, Regular sort
    ##################################################################
+########################
    my $regularStart = Time::HiRes::time;
    my @regularSorted = sort { $compareFunction_in->($transform4Sort_i
+n->($a), $transform4Sort_in->($b)) } @unsortedArray_in;
    my $regularDuration = Time::HiRes::time - $regularStart;
    
    print "Execution time of the Schwartzian Transform: $schwartzianDu
+ration s\n";
    print "Execution time of the Regular     Transform: $regularDurati
+on s\n";

    if (!(@schwartzianSorted ~~ @regularSorted))
    {
        die "Collections are not equal!"
    }

    #print join("; ", @schwartzianSorted);
}
[download]

Next improvements will be with the benchmark. :-) Now that gave a worst result...