Let's suppose you read your "file two" first, like this:

open( P, "<", "Two.txt" ) or die "Two.txt: $!";
my @patches = sort <P>;
chomp @patches;
close P;

my %patch_id;
my $seq_num = 0;
$patch_id{$_} = $seq_num++ for ( @patches );
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That assigns a numeric ID (from 0 to N-1) to each of the N patch names listed in that file, in sorted order. Now read "file one" like this:

my %comp_patch;  # will be a hash of arrays
my $comp_name;   # will store most recently seen computer name

open( C, "<", "One.log" ) or die "One.log: $!";
while (<C>) {
    chomp;
    if ( /^KB\d+/ ) { # this is a patch name
        if ( not exists( $patch_id{$_} )) {
            warn "Computer $comp_name has unknown patch: $_\n";
            next;  # (might want to do something else here)
        }
        $comp_patch{$comp_name}[$patch_id{$_}] = $_;
    }
    elsif ( /^\S+/ ) { # not a patch name, must be a computer name
        $comp_name = $_;
    }
}
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For each computer, you now have an array of patches, with array elements 0 through N-1. But if a given computer did not have a particular patch, the corresponding array index in the HoA structure will be undef. So that is what you check for, to see which patches are missing from each computer:

for my $cname ( sort keys %comp_patch ) {
    for my $pnum ( 0 .. $#patches ) {
        print "$cname lacks $patches[$pnum]\n"
            unless ( defined( $comp_patch{$cname}[$pnum] ));
    }
}
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(untested)