Unfortunately, mobile operating system like Android make the /events approach impossible because the process will just be killed for battery optimization. So pushing is definitely required for those.
The push does not need to contain a lot of data though, so a combination of both pushing and /events is possible too.
Well, exact terminology aside one may see web/app push as a webhook, it's the same principle of delivering messages, but with a different addressing scheme.
But I disagree with the Android part. Androids are the ones who spam my servers with websockets and other things when I restart them, because a user didn't bother to close a page in their browser. Never seen any iOS device doing that.
You could use the server on the receiving end of the web hook to send a notification through the platform's push service. Apps can also be reached via server-sent events, a websocket connection or long polling.
The push does not need to contain a lot of data though, so a combination of both pushing and /events is possible too.