To improve our understanding of high-z galaxies we study the impact of H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ chemistry on their evolution, morphology and observed properties. We compare two zoom-in high-resolution (30 pc) simulations of prototypical $M\star \sim 1010M\odot$ galaxies at $z=6$. The first, "Dahlia", adopts an equilibrium model for H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ formation, while the second, "Alth{\ae}a", features an improved non-equilibrium chemistry network. The star formation rate (SFR) of the two galaxies is similar (within 50%), and increases with time reaching values close to 100 $M\odot /yr$ at $z=6$. They both have SFR-stellar mass relation consistent with observations, and a specific SFR of $\simeq 5Gyr-1$. The main differences arise in the gas properties. The non-equilibrium chemistry determines the H$\to$ H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$~transition to occur at densities $>300cm-3$, i.e. about 10 times larger than predicted by the equilibrium model used for Dahlia. As a result, Alth{\ae}a features a more clumpy and fragmented morphology, in turn making SN feedback more effective. Also, because of the lower density and weaker feedback, Dahlia sits $3\sigma$ away from the Schmidt-Kennicutt relation; Alth{\ae}a, instead nicely agrees with observations. The different gas properties result in widely different observables. Alth{\ae}a outshines Dahlia by a factor of 7 (15) in [CII]~$157.74\mu m$ (H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$~$17.03\mu m$) line emission. Yet, Alth{\ae}a is under-luminous with respect to the locally observed [CII]-SFR relation. Whether this relation does not apply at high-z or the line luminosity is reduced by CMB and metallicity effects remains as an open question.