Genomic instability is considered by many authors the key engine of tumorigenesis. However, mounting evidence indicates that a small population of drug resistant cancer cells can also be a key component of tumor progression. Such cancer stem cells would define a compartment effectively acting as the source of most tumor cells. Here we study the interplay between these two conflicting components of cancer dynamics using two types of tissue architecture. Both mean field and multicompartment models are studied. It is shown that tissue architecture affects the pattern of cancer dynamics and that unstable cancers spontaneously organize into a heterogeneous population of highly unstable cells. This dominant population is in fact separated from the low-mutation compartment by an instability gap, where almost no cancer cells are observed. The possible implications of this prediction are discussed.