  The effective cone of a Mori dream space admits two wall-and-chamber
decompositions called Mori chamber and stable base locus decompositions. In
general the former is a non trivial refinement of the latter. We investigate,
from both the geometrical and the combinatorial viewpoints, the differences
between these decompositions. Furthermore, we provide a criterion to establish
whether the two decompositions coincide for a Mori dream space of Picard rank
two, and we construct an explicit example of a Mori dream space of Picard rank
two for which the decompositions are different, showing that our criterion is
sharp. Finally, we classify the smooth toric 3-folds of Picard rank three for
which the two decompositions are different.
