The absolute value of the current will be the same for both cases. This happens because the MOS structure is symmetrical in general. This means that the bias determines which terminal is the source and which is the drain (for NMOS source at the lower voltage terminal, drain at the higher voltage terminal) and so, when you change the polarity of the 3V, the two terminals are interchanged.
Added after 6 minutes:
If Vg is increased then the current through the MOS/resistor series combination will rise. Also, if the MOSFET was operating in the saturation region for Vg=1 then with Vg=3 it may enter the triode region, depending on both the value of the resistor and the transistor parameters.