The biggest difference is one of intended use. Noria is, first and foremost, a research prototype, intended to explore new ideas in systems research. Materialize, by contrast, is intended to be a rock-solid piece of production infrastructure. (Much of the interesting research, in timely and differential dataflow, is already done.) We've invested a good bit in supporting the thornier bits of SQL, like full joins, nested subqueries, correlated subqueries, variable-precision decimals, and so on. Noria's support for SQL is less extensive; I think the decisions have been guided mostly by what's necessary to run its lobste.rs and HotCRP benchmarks. Make no mistake: Noria is an impressive piece of engineering, but, as an enterprise looking to deploy Noria, there's no one you can pay for support or to implement feature requests.
One area where Noria shines is in partial materialization. Details are in the Noria paper [1], but the tl;dr is that Noria has a lot of smarts around automatically materializing only the subset of the view that is actually accessed, while presently Materialize requires that you explicitly declare what subsets to materialize. We have some plans for how to bring these smarts to Materialize, but we haven't implemented them yet.
Also worth noting is that Materialize's underlying dataflow engine, differential dataflow, has the ability to support iterative computation, while Noria's engine requires an acyclic dataflow graph. We don't yet expose this power in Materialize, but will soon. Put another way: `WITH RECURSIVE` queries are a real and near possibility in Materialize, while (as I understand it) `WITH RECURSIVE` queries would require substantial retooling of Noria's underlying dataflow engine.
One of the creators of Noria, Jon Gjengset, did an interview on Noria [2] that covered some of differences between Noria and differential dataflow from his perspective, which I highly recommend you check out as well!
[0]: https://twitter.com/frankmcsherry/status/1056957760435376129...
[1]: https://jon.tsp.io/papers/osdi18-noria.pdf
[2]: https://notamonadtutorial.com/interview-with-norias-creator-...