Cosmological hydrodynamical simulations, such as EAGLE and IllustrisTNG, provide valuable insights when coupled with high-quality survey data, enhancing our comprehension of galaxy evolution. In this work, we adopt a variance analysis of subsets of continuum-subtracted Sloan Digital Sky Survey (SDSS) spectra by Sharbaf+2023 and evaluate equivalent EAGLE and TNG synthetic spectra. We apply principal component analysis to a homogenous sample of SDSS galaxy spectra in the velocity dispersion range of 100-150km/s, including all three types of galaxies concerning nebular emission, namely star-forming, AGN, and quiescent according to the standard BPT classification. The properties of the spectra are therefore assessed in a model-independent way. We emphasize that the variance of the input data in that work only relates to the absorption lines in the photospheres of the stellar populations. A 3D latent space is defined by the projections of the spectra onto the first principal components. The trends in this latent space support the hypothesis of an evolutionary sequence from star formation to AGN to quiescence. The equivalent data from the simulations reproduce the same trends but with significant overlap between star-forming and AGN galaxies. The spectral fitting analysis of subsets segregated in latent space reveals that PC1 is predominantly influenced by stellar age, with an underlying age-metallicity degeneracy. However, in synthetic spectra, unlike the observed data, metallicity also appears to play a significant role. Moreover, there are substantial differences between the EAGLE and TNG spectral fitting results, as well as their corresponding SFHs. We find that the non-trivial subgrid physics and the effect of different AGN feedback implementations in the simulations control the variance of galaxy spectra. This work illustrates the potential of variance analysis to assess the role of subgrid prescriptions in the spectra.