Amp is not about making your site fast but about making sure that sites aggregated in e.g. Google News are all predictably fast by constraining what they can do. It's not about making the individual sites fast but making sure that none of them are needlessly slow by imposing constraints. Similarly PWA is also not about performance but about adding metadata that phones and browsers can use to treat the site like an ap…
PWAs are much easier to tune for global performance though if you have a tight budget. The app doesn't have to talk much to a Backend server and (down)loading can be tuned by using a CDN.