Suppose that $Y_t$ is a $d$-dimensional symmetric Lévy
process such that its Lévy measure differs from the
Lévy measure of the isotropic $\alpha$-stable process
($0 < \alpha < 2$) by a finite signed measure. For a bounded
Lipschitz open set $D$ we compare the Green functions of the
process $Y$ with those of its stable counterpart, and we prove
several comparability results, both one-sided and
two-sided. In particular, assuming an additional condition
about the difference between the densities of the Lévy
measures, namely that it is of the order of $|x|^{-d+\varrho}$
as $|x|\to 0$, where $\varrho > 0$, we prove that the Green
functions are comparable, provided $D$ is connected. These
results apply, for example, to the relativistic
$\alpha$-stable process. The bounds for its Green functions
were previously known for $d > \alpha$ and smooth sets. Here we
consider also the one-dimensional case for $\alpha \ge 1$, and
we prove that the Green functions for a bounded open interval
are comparable, a case that, to the best of our knowledge, had
not been treated in the literature.