Electrospinning coupled with electrospraying provides a straightforward and robust route toward promising electrospun biocomposite scaffolds for bone tissue engineering. In this comparative investigation, four types of poly(3-hydroxybutyrate) (PHB)-based nanofibrous scaffolds were produced by electrospinning a PHB solution, a PHB/gelatin (GEL) mixture or a PHB/GEL/nHAs (hydroxyapatite nanoparticles) mixed solution, and by electrospinning a PHB/GEL solution and electrospraying a nHA dispersion simultaneously. SEM and TEM analyses demonstrated that the electrospun nHA-blended framework contained a majority of nHAs trapped within the constitutive fibers, whereas the electrospinning-electrospraying combination afforded fibers with a rough surface largely covered by the bioceramic. Structural and morphological characterizations were completed by FTIR, mercury intrusion porosimetry, and contact angle measurements. Furthermore, an in vitro investigation of human mesenchymal stromal cell (hMSC) adhesion and proliferation properties showed a faster cell development on gelatin-containing scaffolds. More interestingly, a long-term investigation of hMSC osteoblastic differentiation over 21 days indicate that hMSCs seeded onto the nHA-sprayed scaffold developed a significantly higher level of alkaline phosphatase activity, as well as a higher matrix biomineralization rate through the staining of the generated calcium deposits: the fiber surface deposition of nHAs by electrospraying enabled their direct exposure to hMSCs for an efficient transmission of the bioceramic osteoinductive and osteoconductive properties, producing a suitable biocomposite scaffold for bone tissue regeneration.