Two-dimensional (2D) cell culture models cannot accurately emulate the three-dimensional (3D) in vivo microenvironment; hence, the shift from compound screening in traditional 2D well plates to 3D cell culture models is forthcoming. New scaffold designs must comply with the 3Rs principle to reduce the use of animal-derived products, such as natural proteins. In line with this motivation, we engineered and compared various fibrous scaffolds featuring diverse fibre networks (coarse and fine fibres) and fibre surface properties (porous vs. smooth fibres), and tested them in in vitro cell culture. We fabricated coarse solid fibre scaffolds via a melt-based electrohydrodynamic process, which resulted in fibres with a diameter of 10.6 ± 1.9 µm and a porosity of 87.1 ± 0.9%. Using solution-based cryo-electrohydrodynamic process, we fabricated fine porous fibre and fine solid fibre scaffolds that exhibited fibres of 2.01 ± 0.5 µm and 1.72 ± 0.6 µm in diameter, with porosities of 96.5 ± 0.3% and 94.4 ± 0.5%, respectively. The scaffolds underwent only chemical modification via an alkaline treatment to enhance their hydrophilicity. We used mouse fibroblast L929 cells and human triple-negative breast cancer MDA-MB-231 cells as cell models, and used the MTT assay to measure their viability. After seven days of cell culture, all scaffolds were thoroughly penetrated. However, the coarse scaffolds created by the melt-based electrohydrodynamic process and the porous fibre scaffolds produced by the solution-based cryo-electrohydrodynamic process outperformed the simpler morphology of smooth fine fibres. Furthermore, the 50% half-maximum effective concentration (EC50) of doxorubicin tested in human glioblastoma (U87-MG) and human triple-negative breast cancer (MDA-MB-231) cell lines in 3D cell culture models was approximately twice as high as that achieved in conventional 2D cell cultures. Therefore, we infer that poly (ɛ-caprolactone) (PCL) microfibre scaffolds, devoid of animal-derived product surface treatment, may provide a favourable 3D milieu for various cell types for in vitro studies.