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Just want to re-emphasize that this point is not just a matter of taste. If you express your causal model (only) as a list of counterfactual statements, there's currently no systematic procedure to find its testable implications. If, however, you write the same model as a DAG...
...not only you can detect those testable implications immediately with the naked eye, but there are efficient algorithms that can find these testable implications automatically for you---both conditional independences, as well as "verma"-type of constraints.
Here are the two step-by-step derivations side by side. The first describes the model in counterfactual statements, and uses consistency and probability theory. The second describes the model graphically and uses d-separation. @yudapearl @autoregress @causalinf 
An addendum for those interested: d-separation requires checking whether every path from X to Z is blocked by Y. The test above is an equivalent simple graphical criterion:
1. prune leaf nodes not in (X, Y, Z)
2. delete outgoing arrows from Y
3. check if X and Z are disconnected
1. prune leaf nodes not in (X, Y, Z)
2. delete outgoing arrows from Y
3. check if X and Z are disconnected
This simple algorithm allows deciding d-separation in linear time and space (in the size of the DAG).
