This study numerically analyzes transient natural convection (NC), heat transfer (HT), and entropy generation (Egen) in a thermally stratified rectangular enclosure and compares the thermal performance of rectangular and square cavities filled with stratified water. The cavities feature a heated bottom wall, stratified sidewalls, and a cooled top wall. The governing equations are solved utilizing the finite volume (FV) scheme for a Prandtl number (Pr) of 7.01 and Rayleigh numbers (Ra) ranging from 10 to 107. The evolution of flow and thermal characteristics is analyzed through isotherms, streamlines, temperature time series (TTS), phase-space trajectories, average Nusselt number (Nuavg), average entropy generation (Eavg), average Bejan number (Beavg), and ecological coefficient of performance (ECOP). The findings indicate that increasing Ra leads to a systematic transition in flow from steady symmetric patterns to fully chaotic motion. Three distinct bifurcations are identified in the rectangular cavity: a pitchfork bifurcation between Ra = 2 × 104 and Ra = 3 × 104, a Hopf bifurcation between Ra = 105 and 2 × 105, and a transition from periodic to chaotic flow between Ra = 5 × 106 and 7 × 106. At the Ra value of 104 to 7 × 106, the quantitative analysis exhibits a higher Nuavg in the square cavity than in the rectangular. However, at Ra = 7 × 106, the Nuavg in the rectangular cavity is 7.21% higher than that of the square cavity. The results demonstrate that the rectangular cavity exhibits a significantly enhanced thermal performance compared to the square.