EM LF solver: Symmetric vs Asymmetric Dirichlet boundary condition

How does the Dirichlet boundary condition at each of the two stimulating electrodes affect the solution?
I tested three cases on an anatomical model: (+1V, 1V); (+2V; 0V) and (0V; 2V); the number pairs mean the boundary condition at either electrode.
In all three cases, the voltage difference between two ends is 2V, but the measured current (flux evaluation) differ significantly. Beside measuring the current, I also placed two sensing electrodes inside the body to measure the voltage drop, and I notice this value also differs significantly in three cases above.