There's certainly a tradeoff between the two approaches; a simpler representation (list of tasks or DAG) is easier to query and manipulate, at the cost of being less expressive, lacking features like loops, conditionals, etc.
In the workflow engine I described, state is represented as a graph of objects in memory; this includes values like integers/strings and data structures like dictionaries/lists, as well as closures, environments, and the execution stack. This graph is serialised as JSON and stored in a postgres table. A more compact binary representation could be added in the future if performance requirements demand it, but JSON has been sufficient for our needs so far. A delta between each snapshot is also stored in an execution log, so that the complete execution history is stored for auditing purposes.
The interpreter is written in such a way that all object allocation, object manipulation, and garbage collection is under its control, and all the data needed to represent execution state is stored in a manner that can be easily serialised. In particular, we avoid the use of pointers to memory locations, instead using object ids for all references. So the persistent state, when loaded, can be accessed directly, since any time a reference from one object to another needs to be followed, the interpreter does so by looking up the object in the heap based on its id.
Non-deterministic and blocking operations (including IPC receives) are handled outside of the evaluation cycle. This enables their results to be explicitly captured in the execution log, and allows for retries to be handled by an external mechanism under control of the user (since retrying can be unsafe if the operation is not idempotent).
The biggest win of using a proper language for expressing the workflow is the ability to add arbitrary logic between blocking operations, such as conditional tests or data structure manipulation. Any kind of logic you might want to do can be expressed due to the fact the workflow language is Turing-complete.