We've done a ton of benchmarking and plan to do more. We have a benchmarking app that exercises various aspects of the binding, templating and dependency-injection modules. This app is used to validate changes we make improve (or at least don't degrade) performance.
There are several posts on the official blog related to performance, here's a couple links:
blog.durandal.io/2015/12/04/aurelia-repaint-perfo…
blog.durandal.io/2015/12/17/more-aurelia-performa…
We're looking at performance from a variety of angles, render speed, memory consumption and cross-browser testing are all important aspects of this work. Recently we uncovered an issue with Edge's promise implementation that was slowing down our initial render in that browser: wpdev.uservoice.com/forums/257854-microsoft-edge-…
In terms of Aurelia vs React, in our testing, it turns out that NG2 is the closest framework to us in terms of all around perf. React is much slower in non-trivial scenarios like dbmonster.