The obvious things are size, speed and integration with existing computers.

A neuron is measured in micrometers, a memristor in nanometers (and the paper suggests even single-atom devices may be possible).

A neuron can fire at most a couple hundred times per second; a memristor has "subnanosecond switching speed", i.e. it operates in the usual GHz operating frequency range of modern computers.

And you can integrate them at the circuit level, so they can draw on the superbiological capabilities of existing computers at native speed.