Are statecharts with parallel states NFA, DFA, or none of the above?
The paper Parallel Finite Automata for Modeling Concurrent Software Systems contains a proof and examples showing that a (non-hierarchical) parallel state machine can be converted into a non-parallel version. The technique is somewhat obvious: simply create the cartesian product of all concurrent sections and you have a DFA.

Combine with a proof that any hierarchical section of a state machine can be flattened into an equivalent non-hierarchal version, and there exists an obvious—but hard for me to formally notate—conversion process that involves flattening hierarchies and expanding parallel sections from the leaves on upwards.

The result is that any SCXML state machine can be converted into an equivalent version that contains neither hierarchy nor parallel states. At this point the state machine may be DFA, NFA, or NFA with ε-moves (depending on the transitions used), but all of these are similarly equivalent.

In summary, I believe that any SCXML state machine can be converted into an equivalent DFA, and as such the formalisms of DFA apply.