Web-push as a service always grows.
About two weeks ago Google made available option rich-push with two buttons and a bigger picture (from 1360px to 1020px).
Examples that already use rich push or testing it in the demo:
1) How it can look on Retina display
2) On a regular
Push like that will be a part of a premium subscription, but now it is available for free for all the Push.World clients. With the only restriction — we deliberately limited auto-mailing with large pictures.
And one more beautiful push MacDigger:
How to send out rich-push
2. Or create a copy of a sent push.
3. Find in the menu Rich push new element that downloads pictures.
4. Paste a picture (1360 px on 1020 px).
5. Send out
Today almost 85% of Chrome-browsers allows pushes with a big pic. So for that reason, don't be afraid that someone will miss a push notification from you.