Quite often, the RS232 <-> RS485 converters use either the CTS/RTS and/or the DSR/DTR RS232 handshaking signals to control the transmit/receive functions of the RS485 transceiver chip(s). It is possible that the USB-RS485 converter is either not using these signals, or not using them properly -- possibly because of an issue with the driver or driver configuration settings for the port.
Are you using the USB converter in the same way as the RS232-RS485 converter (for example, using Hyperterminal or PuTTY or other terminal emulator program with both devices)? Do both devices appear as Virtual COM Ports (VCP) within Windows ? Are you using Windows, or some form of Linux, or Mac OS on your computer?