The sorting of keys (or, lines) does not help as the output would be out of sync from the order in a file. OP's code (after rewinding the file handle) would have printed the difference in lines in the same order as the lines appear in a file.

Use of hash in OP was a handy way to keep track of lines seen. I think to keep the order of lines printed was the reason that coding_new opened the same files twice. I personally would have generated the hash with line as key & $. as value. To print, then I would have sorted on the hash value. I personally would have used Algorithm::Diff.