Dimensional check: Hydraulic head (h) is always expressed as a length (cm, m), the same unit used for the height of water in a tensiometer or piezometer.
Potential energy per unit weight has units of \( \frac{\text{energy}}{\text{force}} = \frac{\text{N}\cdot\text{m}}{\text{N}} = \text{m} \), that is, a length. This matches the physical unit of hydraulic head exactly.
Energy per unit mass gives \( \text{J/kg} = \text{m}^2/\text{s}^2 \) (a specific potential, not head), and energy per unit volume gives \( \text{J/m}^3 = \text{Pa} \) (a pressure, not head). Since only the per-unit-weight form reduces dimensionally to a length, hydraulic head is defined as potential energy per unit weight of soil water.