The primary learning mechanism of artificial neural networks (ANN) is back-propagation, which is not biologically plausible.
Trevor Berkolay created an alternative to this learning with the Neurological Engineering Framework (NEF) and Nengo called hPES (Homeostatic Prescribed Error Sensitivity) . But how does it's learning capabilities compare to the standard supervised and unsupervised learning of ANNs in terms of computational power required and speed of learning?
 See also, "How to Build a Brain" by Chris Eliasmith chapter 6.4
Note: I realised that this question portrayed ANNs and the NEF as adversarial, which really isn't the case. Spaun the brain model, which is kind of the poster child of the NEF, uses ANNs (Deep Belief Networks specifically) converted into spiking neurons in it's vision system.