A great successor to Vimperator is on the works now:
For example, Opera and Firefox support the Sidebar API, which allows essentially arbitrary HTML pages to be placed in, you guessed it, a sidebar. Chrome does not support this, because they supposedly just don't want to have sidebars in their browser (it's not exactly an unsolvable task to implement).
Overall, Firefox will support the most extension APIs, but even there not all extensions will work, because there's always going to be some APIs that only make sense in one specific browser.
Lastly, it is necessary for the extension authors to port their extension. The work they have to do for porting might often be as minimal as just repackaging, testing and then uploading to the other browser's extension webpage, but they do have to do it.
So, this is going to cut off many extensions, too. If they're unmaintained, no one's going to port them. And Mozilla has much stricter policies for telemetry, ads etc. in extensions, too, so another chunk of extensions won't get ported for that reason.
If there is a specific Chrome extensions that you care for getting ported and it's unmaintained, then you can try it with Chrome Store Foxified [1], which will do the repackaging automatically. The testing you'll have to do yourself and then the fixing of potentially broken things and uploading, that depends on the license of the extension, if you're allowed to do that.
[1] https://addons.mozilla.org/en-US/firefox/addon/chrome-store-...
Qutebrowser keybindings essentially have full control over the page at all times.
It's going quite slow however...
However, each browser vendor has their own specific additions, and hopefully Mozilla will add some things addons like Vimperator would need, see e.g. https://bugzilla.mozilla.org/show_bug.cgi?id=1215061