Well-ordered 2-dimensional (2D) hexagonal and 3-dimensional (3D) cubic mesoporous silicon oxide thin films prepared using triblock Poly(ethylene oxide)-Poly(Propylene oxide)-Poly(ethylene oxide) copolymer species (P123, F127) as the structure-directing agents, are studied by positron beam analysis in parallel with X-ray reflection measurements. It is observed that in the two films with equivalent porosity and pore size (normal to the film surface direction), the shape of mesopores considerably affects positron annihilation behavior. The narrowed positron annihilation Doppler broadening in the 2D hexagonal mesoporous film may suggest a higher positronium formation probability there, owing to a larger effective open volume area originated from the extension of pore channels parallel to the film substrate.