The advantage of the BrHalf4W circuit is that the effect of lead resistance is measured and compensated for. The disadvantage is that it requires two differential (four single-ended) voltage input channels and four wires to the sensor.
Some sensors have four wires and are sensitive enough that the lead resistance would cause too great an error.
The BrHalf, a two-wire measurement, does not compensate for lead resistance.
The BrHalf3W lead compensation assumes that both leads are of the same resistance.