For the purpose of this analysis suffices to say that modular construction delivers on-site fully ready "boxes" (ready from outside and inside). On-site work is reduced to a minimum.
Yet, depending on the architecture of the building, some works have still to be performed after the installation of the modules.

NOTE: modules are always built using prefab elements or frames.

Building with modules limits the freedom when it comes to architectural solutions. 
Modules take more time (and money) to be designed and more time to be produced.
Of course, time is saved on-site but the overall length of the project is comparable with element construction.

In general, one should go for modules in case of very large projects (apartment buildings with repetitive architectural patterns) or in the case when time on-site is an issue (i.e demolishing existing house to replace it with a new one).

In all other cases, element construction will be a better solution since it is more flexible and it comes at a comparable price and time of implementation.