When comparing a relay to a Mosfet there are a number of significant differences. Some of them are:
- The relay is fully isolated between coil to contacts. A Mosfet is not. You would not want to do this but if you connected one lead of the coil to one of the contacts you would have something approaching the lack of isolation of the Mosfet.
- A relay contacts have no polarity consideration, a Mosfet does.
This means you cannot indiscriminately put a Mosfet where you could have added a relay contact. You must worry about the lack of isolation, polarity and the voltages required to be able to control the Mosfet from your arduino.