An accurate assessment of white dwarf cooling times is paramount so that white dwarf cosmochronology of Galactic populations can be put on more solid grounds. This issue is particularly relevant in view of the enhanced observational capabilities provided by the next generation of extremely large telescopes, that will offer more avenues to use white dwarfs as probes of Galactic evolution and test-beds of fundamental physics. We estimate for the first time the consistency of results obtained from independent evolutionary codes for white dwarf models with fixed mass and chemical stratification, when the same input physics is employed in the calculations. We compute and compare cooling times obtained from two independent and widely used stellar evolution codes, BaSTI and LPCODE evolutionary codes, using exactly the same input physics for 0.55M_{sun}_ white dwarf models with both pure carbon and uniform carbon-oxygen (50/50 mass fractions) cores , and pure hydrogen layers with mass fraction qH=10^-4^M_WD_ on top of pure helium buffers of mass qHe=10^-2^M_WD_.