The biggest difference the memristor brings is to Machine Learning. The memristor is a first step towards a hardware implementation of Hebb's rule - "neurons that fire together wire together". Hebb's rule variants are used in machine learning algorithms to do things like web-search, image/object recognition, etc. (Specifically, Hebb's rule can be used to compute PCA.)

It's interesting to note that the brain does not have separate components for memory and computation. Every neuron computes and stores at the same time.