use Data::Dumper;
print Dumper($hComData);
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Your sort looks very strange:

    my ($chn, $ex) = sort ($hEntry->{chain}, $hEntry->{exists});
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If you don't need a Hash-of-Hashes, just use a simple hash.

I tried 'diff' -the trouble there is that the items in the two files don't always appear in the same order. It simply doesn't work. I'll take a peak at the links you suggested though.

By using a hash as per the FAQ, the intersection/difference calculation will be order-independent. You will have to compare the resulting hash (called %count in the FAQ) against a given file's content to determine which file lacked the line in question. Note that the FAQ's code fails if either array has repeat entries.

Alternatively, you can use bit operations rather than simple incrementation to encode a little extra info. The FAQ code structure is more immediately obvious, but this may do more of what you want:

#!/usr/bin/perl
use strict;
use warnings;

my $master = shift;
my $completed = shift;

open my $mh, '<', $master or die "Open fail on $master: $!";
my @master_lines = <$mh>;
chomp @master_lines;

open my $ch, '<', $completed or die "Open fail on $completed: $!";
my @completed_lines = <$ch>;
chomp @completed_lines;

my %count;

for my $element (@master_lines) {
    $count{$element}|=1;
}
for my $element (@completed_lines) {
    $count{$element}|=2;
}

print "$master only:\n";
for my $element (@master_lines) {
    next if $count{$element} & 2;
    print "$element\n";
}

print "$completed only:\n";
for my $element (@completed_lines) {
    next if $count{$element} & 1;
    print "$element\n";
}
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There are already several tools to achieve what you want, writing your own is probably needless.

A standard Unix-like solution (works under bash):

$ diff <( sort master ) <( sort completed ) | grep '^<' | cut -d ' ' -
+f2-
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Depending on your needs you may want to use sort -u instead of a simple sort.

Or if you're under some Debian-derivative distro just install the moreutils package and use combine:

$ combine master not completed 
1ao8A
1jkxA
1juvA
1mejA
1meoA
1n0uA
1pjqA
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Hope that helps.

diff file1 file2 > diff.out
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I would probably do something like the following:

#!/usr/bin/perl
#
use strict;
use warnings;

(@ARGV == 2) or die "USAGE: $0 master complete\n";
my ($master, $complete) = @ARGV;

open(my $fh_complete, '<', $complete) or die "$complete: $!";
open(my $fh_master,   '<', $master  ) or die "$master: $!";

my %complete = map { $_=> 1 } <$fh_complete>;

my @incomplete = grep { !$complete{$_} } <$fh_master>;

print @incomplete;
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update: kennethk pointed out in a private message that the requirement might be an XOR operation (to paraphrase: all lines from both files (master and complete) that are not in both files), rather than all lines in the master file that are not also in the complete file. The program above provides the latter.

update: maybe it would be clearer to say: all lines that appear in either and only one of the two files. It is difficult to be both simple and unambiguous with English.

$ perl -nle '(1..eof)?$h{$_}++:$h{$_}||print' completed master
1ao8A
1jkxA
1juvA
1mejA
1meoA
1n0uA
1pjqA
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(sorry, couldn't resist golfing :)

I tend to encounter problems of this type so often in my work that I wrote a very general tool to address it -- you can find it here: cmpcol.

It allows that one or both input lists may actually be flat tables (possibly with varied field delimiters), where just one or more columns are of interest for doing the set-arithmetic.