Melt extrusion 3D printing has become an attractive additive manufacturing technology to construct degradable scaffolds as tissue precursors in order to create clinically relevant medical devices. Towards this end, a commonly used synthetic polyester, poly-caprolactone (PCL), was used to make scaffolds composed of different biomaterial compositions to increase bioactivity using 3D melt pneumatic extrusion technology. Varying ratios of the natural biopolymer, chitosan, or the bioceramic, β-tricalcium phosphate (TCP) were blended with PCL to fabricate support scaffolds with three-dimensional (3D) architecture for human bone-marrow derived mesenchymal stem cell (hBMSC) growth for potential bone regeneration application. In this study, basic printing requirements as well as biomaterial dynamic mechanical (DMA), elemental, and thermogravimetric (TGA) analysis results demonstrate material homogeneity as well as thermal stability. Scaffold morphology and microarchitecture were assessed using scanning electron microscopy (SEM) alongside in vitro scaffold degradation and biological characterisation. Human BMSC proliferation was assessed using fluorescence imaging, and quantitated via the 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide (MTT) colorimetric assay. These in vitro cell viability studies revealed that the highest chitosan concentration blend of 20% favoured the most hBMSC growth, exhibited the most swelling, and showed minimal degradation after 28 days. The 20% TCP blend had the second highest hBMSC growth, exhibited moderate swelling, and the fastest degradation rate. Overall, this study demonstrates the first direct comparison of a natural biopolymer-based, that is, chitosan, 3D melt extruded PCL composite with that of a bioceramic-based, that is, β-TCP, PCL composite and their effects on hBMSC 3D proliferation. 3D melt extruded PCL-based composite scaffolds methodology offers a straightforward way to print scaffolds with good shape fidelity, interconnected porosities and enhanced bioactivity; and demonstrates their potential use for regenerative, bone repair applications.