If you got the null modem cable fully wired with RTS/CTS handshaking pins connected there shouldn't be any transfer errors. There is no need to change much in the terminal programs except making sure you set the same speed, data bits, parity and stop bit (eg. 19200 8/N/1) and enable hardware handshake (CTS/RTS) on both sides. Then use ZMODEM protocol for the file transfer.
http://www.nullmodem.com/NullModem.htm
Are you using some kind of "USB to serial" interface on the PC side? Those can be tricky with the RTS/CTS support.