In the context of a large animal model of early osteoarthritis (OA) treated by orthobiologics, the purpose of this study was to reveal relations between articular tissues structure/composition and cartilage viscoelasticity. Twenty-four sheep, with induced knee OA, were treated by mesenchymal stem cells in various preparations—adipose-derived mesenchymal stem cells (ADSCs), stromal vascular fraction (SVF), and amniotic endothelial cells (AECs)—and euthanized at 3 or 6 months to evaluate the (i) biochemistry of synovial fluid; (ii) histology, immunohistochemistry, and histomorphometry of articular cartilage; and (iii) viscoelasticity of articular cartilage. After performing an initial analysis to evaluate the correlation and multicollinearity between the investigated variables, this study used machine learning (ML) models—Variable Selection Using Random Forests (VSURF) and Extreme Gradient Boosting (XGB)—to classify variables according to their importance and employ them for interpretation and prediction. The experimental setup revealed a potential relation between cartilage elastic modulus and cartilage thickness (CT), synovial fluid interleukin 6 (IL6), and prostaglandin E2 (PGE2), and between cartilage relaxation time and CT and PGE2. SVF treatment was the only limit on the deleterious OA effect on cartilage viscoelastic properties. This work provides indications to future studies aiming to highlight these and other relationships and focusing on advanced regeneration targets.