Acoustic Velocity Horns (AVHs) are acoustically small funnels open to incident acoustic waves from mouth and throat (for single horns) or both mouths for double horns. Unlike traditional pressure horns terminated at the throat, AVHs yield appreciable amplification of the particle velocity across a wide frequency range starting from extremely low infrasound frequencies. Such horns can be utilized to enhance the performance of conventional vector and acoustic intensity sensors. The present paper includes derivation of directional properties and gains for acoustic velocity as well as pressure for horns of various configurations: single and symmetrical double-horns, and symmetrical horns with inserts of various profiles. The study reveals that the conical double-horns provide the highest velocity gain as compared to horns with an exponential profile or with inserts. The maximum gain cannot exceed a horn's mouth-to-throat radii ratio. In addition to the velocity gain, AVHs offer dipole directionality for the particle velocity and omnidirectional response with no gain for acoustic pressure. These findings were experimentally validated using a water-submerged conical double-horn.