If the input files are sorted (or if you use an external tool to sort them before running the Perl script), a very memory-efficient algorithm can be used:

my ($f1_k1, $f1_k2);
my ($f2_k1, $f2_k2);

my $f1_line;
my $f2_line;

my $regexp = qr/^((\w+(?:\s+\w+){3})(?:\s+\w+){3}(.*)/;

for (;;) {
   # Read from FILE1 if appropriate.
   if (not defined $f1_line) {
      $f1_line = <FILE1>;
      last unless defined $f1_line;

      # Extract the keys for comparison.
      ($f1_k1, $f1_k2) = $f1_line =~ $regexp;

      # Make sure the regexp matched.
      if (not defined $f1_k1) {
         undef $f1_line;
         next;
      }
   }

   # Read from FILE2 if appropriate.
   if (not defined $f2_line) {
      $f2_line = <FILE2>;
      last unless defined $f2_line;

      # Extract the keys for comparison.
      ($f2_k2, $f1_k2) = $f2_line =~ $regexp;

      # Make sure the regexp matched.
      if (not defined $f2_k1) {
         undef $f2_line;
         next;
      }
   }


   # Do the comparisons.
   my $cmp = $f1_k1 cmp $f2_k2;

   if ($cmp == 0) {
      print("Key 1 match:\n");
      print("$f1_line\n");
      print("$f2_line\n");

      if ($f1_k2 eq $f2_k2) {
         print("...and key 2 matches.\n");
      } else {
         print("...but key 2 doesn't match!\n");
      }

      # Only read from one file in case of duplicate keys.
      undef $f2_line;
   }

   # Need to read from FILE1.
   undef $f1_line if $cmp < 0;

   # Need to read from FILE2.
   undef $f2_line if $cmp > 0;
}
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(The code isn't tested, but the idea is sound.)