In general, decomposition simplifies the modeling process because it divides the parallel system into parts that are more amenable to modeling. The main difference among the decomposition strategies is how the system is divided and the implications of the division.
Vertical and horizontal decompositions are limited by the interfaces between the pieces. In horizontal decomposition, the interfaces limit the range of applications that can be treated by the model. In vertical decomposition, the model for each piece does not consider the influence of the pieces that precede it, which can lead to considerable inaccuracy. Decomposition by overhead does not have this interface limitation, because it usually assumes that the categories are mutually exclusive. Also, note that decomposition does not address the problems or limitations of the underlying techniques used to model the pieces.
Decomposition helps identify those parts of the parallel system or application that present problems, and facilitates analysis of those parts in isolation. However, we still have to understand the interactions among those parts (e.g., system layers, high-level operations).