The source of the stress could be related to the further processing on top of the the thin film such as coating with resist, stripping the resist, baking, UV exposure, or oxygen plasma.
I fear your question may be to general, as the answer varies with the kind of crystalline or amorphous configuration and the applied stress. Many materials don't have "one" crystalline phase. Take Ge2Sb2Te5 for an example it has a hexagonal and a metastable fcc phase and if you crystallize it very quickly it even may have a rock salt phase. So which of them do you want to take as a reference for comparison to the amorphous phase? And amorphous phases are also not always similar. For said GeSbTe there is a significant difference between an as deposited and a melt quenched amorpheous state (can be recrystallized easier).
Another question is the crystalline film monocrystalline? How thick is the film? Are there other defects...
Oh and until now we were only looking at thermal stability. This question may easily occupy a whole research institute for a decade.
If by tolerating stress you mean whether thin film can be cracked along a certain direction, then the general answer is that crystalline materials have well defined cleaved edges, which means it can be broken align certain crystalline directions, while well defined cleaved edges are absent in amorphous materials. That is why flexible electronics and solar cells are often made of amorphous materials rather than single crystalline materials.
Hi! Based on my experience, under the same circumstance, same composition, same film thickness, same substrate, same multi layer stack and same... hah, amorphous film has more stress tolerance.