For clathrate-hydrate polymorphic structure-type (sI versus sII), geometric recognition criteria have been developed and validated. These are applied to the study of the rich interplay and development of both sI and sII motifs in a variety of hydrate-nucleation events for methane and H2S hydrate studied by direct and enhanced-sampling molecular dynamics (MD) simulations. In the case of nucleation of methane hydrate from enhanced-sampling simulation, we notice that already at the transition state, ∼80% of the enclathrated CH4 molecules are contained in a well-structured (sII) clathrate-like crystallite. For direct MD simulation of nucleation of H2S hydrate, some sI/sII polymorphic diversity was encountered, and it was found that a realistic dissipation of the nucleation energy (in view of non-equilibrium relaxation to either microcanonical (NVE) or isothermal-isobaric (NPT) distributions) is important to determine the relative propensity to form sI versus sII motifs.