A difference between the two is that LSTM has a constant amount of memory, defined at training time. In this model, the stacks can grow arbitrarily large. Also

A difference between the two is that LSTM has a constant amount of memory, defined at training time. In this model, the stacks can grow arbitrarily large. Also, using a finite state machine and two stacks one can simulate any Turing machine, so one can represent arbitrary computations in this model (assuming we structure the input in such a way that there is time to do the computation in question).