The MVI71 module doesn't provide the same functionality as the 1785-ENET.
The Prosoft MVI71 module allows reads and writes of an emulated PLC-5 data table inside the module itself. That data is moved to the real PLC-5's data table using block transfer instructions.
The Allen-Bradley 1785-ENET module adds an actual Ethernet communication port to the controller's operating system and allows full access to all of the real data tables and the controller OS, which allows you to go online, upload/download, edit, etc.
For this particular controller, your options are to replace the MVI71 with a 1785-ENET, use a serial/Ethernet converter like the 1761-NET-ENI on the serial port, or use a DH+/Ethernet bridge like the ControlLogix 1756-DHRIO and 1756-ENBT modules.