Are there directories inside the directories? If so, I don't think the file glob method will count them all. It will just count the files inside the top-level directory (it will count directories, too, but not go down inside them).

I'd do something like this:

use File::Find;
my $category;
for my $file (@file_list) {
  my $file_path = dirname($file); # better make sure this is working!
  my $count = CountFiles($file_path);
  if ($count < 200) {
    $category = "paper";
  } else {
    $category = "collection"
  }
}

# Count all files contained inside a directory, recursively
sub CountFiles {
  my $dir = shift;
  my $count = 0;
  find( sub {
    if (-f) { # only count regular files
      ++$count;
    }
  }, $dir);
  return $count;
}
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Note that this way you can do things like not count zero-length files, or ignore symbolic links, etc. by simply changing the file test performed inside the 'find'.