The femtosecond and picosecond excited-state dynamics of pyrazine are studied using full-dimensional trajectory surface hopping (TSH) dynamics simulations. We assess how different types of potential energy surfaces (PESs) influence the simulated dynamics; these include on-the-fly potentials versus those obtained by the linear vibronic coupling (LVC) model, calculated by multistate multiconfigurational perturbation theory (MS-CASPT2) and time-dependent density functional theory (TD-DFT) as well as machine-learning (ML) PESs. We find that MS-CASPT2 delivers a reliable excited-state description utilizing on-the-fly and LVC PESs for short (fs) and long (ps) timescales, respectively. TD-DFT (B3LYP) provides qualitatively accurate dynamics for short timescales but is unable to account for the coupling with the ground state and is even qualitatively wrong for longer timescales (i.e., failing to account for the internal conversion to the ground state). We observe and rationalize the oscillations (with a period of #40 fs) in the populations of 1B3u (n#*) and 1Au (n#*) excited states. Both MS-CASPT2 and TD-DFT-based TSH simulations identify significant singlet-triplet intersystem crossing (ISC) on picosecond timescales (#10 ps). With our simulations, we established the excited-state mechanism both for the internal conversion to the singlet ground state and singlet-triplet ISC that involves the 1B3u (n#*) and 1Au (n#*) states with similar weights. Finally, we successfully used pyrazine as a benchmark model for TSH carried out on ML-PESs.