We study the chemical evolution of the disks of the Milky Way (MW) and of Andromeda (M31), in order to reveal common points and differences between the two major galaxies of the Local group. We use a large set of observational data for M31, including recent observations of the Star Formation Rate (SFR) and gas profiles, as well as stellar metallicity distributions along its disk. We show that, when expressed in terms of the corresponding disk scale lengths, the observed radial profiles of MW and M31 exhibit interesting similarities, suggesting the possibility of a description within a common framework. We find that the profiles of stars, gas fraction and metallicity of the two galaxies, as well as most of their global properties, are well described by our model, provided the star formation efficiency in M31 disk is twice as large as in the MW. We show that the star formation rate profile of M31 cannot be fitted with any form of the Kennicutt-Schmidt law (KS Law) for star formation. We attribute those discrepancies to the fact that M31 has undergone a more active star formation history, even in the recent past, as suggested by observations of a head-on collision with the neighboring M32 galaxy about 200 Myr ago. The MW has most probably undergone a quiescent secular evolution, making possible a fairly successful description with a simple model. If M31 is more typical of spiral galaxies, as recently suggested by Hammer et al. (2007), more complex models, involving galaxy interactions, will be required for the description of spirals.