So basically they are all programmable, operates in parallel, with small blocks capable of acting like connected state machines. What's the big deal with neuromorphics chips?
It's a big question, much too large to answer here, but here are two elements:
different building blocks: neuromorphic chips wouldn't be useful without a theory behind them. So they're made with the aim of transfering neural network models to them, and they try to offer the best building blocks for that: neurons, synapses, etc. Typically a pure hardware (analog) neuron is built around a capacitor and FPGAs don't provide that.
massive connectivity: FPGAs can only provide a limited amount of interconnects. 80% of your brain is just wires (white matter) and the remaining 20%, where the neurons are, also contains lots of wires. Neuromorphic chips are made to provide a large communication bandwidth, and to cope with communication patterns that are irregular and divergent (meaning many of the assumptions behind a standard computer's memory access model, like caching and reading memory in chunks, don't hold any more).
Note that not all neuromorphic chips are based on analog neurons. For instance the SpiNNaker project uses lots of small ARM CPU cores (each running 100-1000 software neurons) together with a specialised mesh network.