Common gate amplifier with load connected to negative DC bias
The two circuits are equivalent except:

The voltage accross the capacitor.  In this case it looks like the capacitor needs to be able to handle Vdd volts either way but with different polarity.  If you know something particular about the bias point and the amplitude of the signals, then you might possibly be able to get a away with a lower voltage capacitor in one of the cases.

Where the load current flows.  The Vdd current requirement could be different between the cases.

The effect of noise on Vdd.  Case B is more susceptible to this than case A.



In both cases the signal accross Rl is the same, assuming no significant noise on Vdd.