  We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about
the ratio of the classical and pluricomplex Green functions to the case of
$\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type.
We also give some lower estimates. In order to obtain those results, and
because it is of independent interest, we refine and unify some classical
estimates about the Kobayashi distance and the Lempert function in such
domains.
