Aren't both Chrome and Firefox's sync protocols open? At least, the Firefox Sync server is still self-hostable and open source, and at least the client side of Chrome's sync is open source since Chromium can sync as well...
I've never understood why someone didn't implement a Firefox Sync extension for Chrome or vice-versa. Is it technical or are people opinionated enough about browsers that no one has the personal need to develop such extensions?