Despite having very similar bulk properties such as glass-transition temperature (Tg), density, and fragility, polystyrene (PS) and poly(methyl methacrylate) (PMMA) exhibit characteristically different Tg depression in free-standing ultrathin films due to free surface effects. Here we explain this difference using our recently established chemistry-specific coarse-grained (CG) models for these two polymers. Models capture the dissimilar scaling of Tg with free-standing film thickness as seen in experiments and enable us to quantify the size of the regions near free surfaces over which chain relaxation exhibits differences from bulk. Most interestingly, vibrational density of states (VDOS) analysis uncovers a relationship between the amplitude of side-chain fluctuations, associated with side-chain flexibility and Tg-nanoconfinement. We discover that increasing backbone to side-chain mass ratio in CG models increases the amplitude of side-chain fluctuations and suppresses the free-surface effect on Tg. We show that mass distribution and side-chain flexibility are central to explain dissimilar free surface effects on PS and PMMA. Our model predictions are further corroborated by experimental evidence showing the role of mass distribution in styrene thin films. Our study ascertains the significance of molecular characteristics on nanoconfinement and highlights the ability for chemistry-specific CG models to explore the thermomechanical properties of polymer thin films.