Actually RS232 Data Logger will work with any COM port no matter which cable is used. As can be derived from its features page "RS232 Data Logger is an Open Source application which allows you to redirect all communication data from RS232 compliant serial port device into a text file for further analysis." So, there is no difference for this freeware which cable or device is connected to the serial port since it logs the data from RS232 port.
To download free RS232 Data Logger with sources and User Manual visit: http://www.eltima.com/products/rs232-data-logger/