Sorry for the delayed response here. I was speaking before on a neuron-for-neuron basis. In computation-theoretic terms, I presume a spiking neural network mod

Sorry for the delayed response here. I was speaking before on a neuron-for-neuron basis. In computation-theoretic terms, I presume a spiking neural network model such as Izhikevich E.M. (2003) is equally powerful to a rate-based model such as Graves et al. (2014), in that they're both equivalent to a Turing machine. (At least I assume Izhikevich's model can be, though I'm not aware of any proofs or demonstrations of it performing arbitrary computations.) Also, keep in mind that saying something is 'Turing complete' only says that a machine is capable of computing anything that any other universal Turing machine can perform. It doesn't say anything about how efficiently it can do it. For example, a conventional computer and a quantum computer can both do integer factorization. But a quantum computer can do it much more efficiently, being able to do it in polynomial time. A quantum computer is therefore more powerful, even if they're both equivalent machines in computation-theoretic terms.