As a Linux user I have never used Evernote, but Google Keep has cross-device persistent notes and I've never had even the tiniest glitch with synchronization.
Google Keep works offline, it has seamless syncing when it is online and I can access it from all my devices (including my phone).
I guess you don't consider a Chrome App to be a "real" native app and that somehow makes it different for you, but I don't see any meaningful distinction.
Evernote native vs web Sublime Text vs Atom Mail Client vs Web mail etc.
Not native, but feels close enough for this type of thing to me.