For instance, we tried to propose Matrix as the basis of bluesky (hence https://matrix.org/blog/2020/12/18/introducing-cerulean/) - but obviously they went and built atproto instead. Meanwhile, both projects have effectively taken VC funding (Element, founded by the core Matrix team has raised from VCs - although Matrix itself is governed by the independent non-profit Matrix.org Foundation). I'm honestly entirely sure how they contrast together :D