Shtukas were defined by Drinfeld as a generalization of Drinfeld modules. While the relationship between the definitions of Drinfeld modules and shtukas is not obvious, one does have a natural bijection between Drinfeld modules and shtukas with two legs satisfying a nilpotence condition on one leg (or something like that). Since that time, a lot of research has been done involving Drinfeld modules and involving shtukas.
What I would like to understand is what the implication is of the relationship between Drinfeld modules and shtukas for this work. I don't usually see researchers working on one of the two kinds of object discuss the relation of their work to the other object. To make my question precise, let me ask:
For what problems is it crucial that we work with Drinfeld modules and not shtukas? For what problems is it crucial that we work with shtukas and not Drinfeld modules? Why?
For instance, I know that Drinfeld proved Langlands for GL_2 with Drinfeld modules, and Lafforgue proved it for GL_n with shtukas. Is it impossible to make a similar argument work with Drinfeld modules for GL_n, or is it more a matter of convenience?
In the reverse direction, the proof of Langlands for GL_2 by Drinfeld modules seems to give a slightly stronger statement than the proof by shtukas. In the Drinfeld module case, the desired Galois representation appears inside the cohomology of the 1-dimensional Drinfeld modular curve, while I think the relative moduli space of Shtukas for $GL_n$ is $2n-2$ dimensional, so $2$-dimensional in the case of $GL_2$. Because every Galois representation appearing in the cohomology of a curve appears in the cohomology of a surface, but not vice versa, Drinfeld's is (I believe) a stronger statement than Lafforgue.
I ask for a modern perspective because I want an answer informed by some of the research that has been done since Drinfeld defined shtukas, rather than a purely abstract description of the relationship.