The cheap chinese ethernet-to-RS232 bridge has a function similar to Lantronix X-port, but I don't believe that you can seriously expect long term availibility.
The WIZnet chips are a different kind of ethernet interface. They would be used if you want to add more than a simple serial port over ethernet, e.g. multiple ports or specific protocols that can't be implemented witha an ethernet RS232 adapter.
The decision depends on the intended product functionality.