Here is the critique from one of the Jaina texts:
Buddhist: This World is made up of Five Skandhas. These Five Skandhas arise and fall momentarily. The World is also like that, is in a state for Momenatiriness, it is in a false state. It changes every moment.
Jain: Yes. This is your Kshanabhangavada. By this, you say that materials die out before, they are formed again. By this, each event does not have any relation with the earlier events. You call this as Asat Karyavada. If this is so, then there is no Causality between events. If that is so, then this is no obstruction for an Impossible event like "Apperance of a Flower in the Sky" (Akasha Pushpa). Is it not so ?
If Vasana can be considered as an link for Casuality, we must accept some kind of relation between events. Kshanabhangavada cannot be true.
This seems an early criticism consistent with what I know of Jain thought. There are some very big differences between the two theories of causality. My understanding is that, for Jains, primary causality (upādanā kārana) is material, i.e., body and material surroundings, with the assumption that the effect is present in the cause. Nāgārjuna's Mulamadhyamakakarika is, in part, is a later refutation of such views.
The above is a poor criticism, however. It is based in only a partial understanding of Buddhist thought. It is correct that, in Buddhist philosophy, each phenomenal moment contains its own destruction rather than requiring some tapas (spiritual austerity) to destroy a thought arisen from material circumstances. The three "moments" of thought are the immediate past, the present, and the "arising" moment, with each being causally connected, but each moment expires without need for mental intervention. Further, as tomamundsen implies, it ignores the Buddhist tenet of pratītyasamutpāda, or co-dependent arising, which demonstrates the 12 nidana (links) in the chain of causation. Śīla, discipline, is required to "break" the causal chain, however, so the two lines of thought are similar in that regard.
While Buddhist logic recognizes the category of abhāva-padārtha (impossible things), such as "the hare's horns" or "the son of a barren woman", it is precisely the momentary nature of phenomenal thought that allows such vikalpa (incorrect notion) to be replaced by pramāṇa (correct perception).