Due to their high mobility and direct band gap, III-V materials promise good prospects of obtaining novel, high-performance devices for electronic and photonic applications. In this paper, two variants of the established Template Assisted Selective Epitaxy (TASE) technique - are explored to study the structural quality of GaAs and InGaAs microcavities monolithically integrated on Si (001). The first variant involves a one-step direct cavity growth (DCG), while the second relies on a two-step virtual substrate (VS) growth approach. The cavities obtained were investigated by Scanning Transmission Electron Microscopy (STEM) and Energy Dispersive X-Ray Spectroscopy (EDX); the findings have been correlated with the photoluminescence properties of the cavities. Both approaches enable monolithic integration of GaAs crystalline material in predefined oxide microcavities. In some cases, they allow the III-V materials to be grown as a single gain and do not lead to noticeable structural defects. InGaAs disks and ring cavities grown using the VS approach have also been investigated. Despite the presence of planar defects and rough surfaces, lasing could be achieved at low temperature.