Happy to share some experience here, since push advertising trips up a lot of beginners at first.
The core difference comes down to opt-in vs. no opt-in:
Classic Push requires users to subscribe before they start seeing notifications in the tray or on the lock screen. Because they've actively opted in, this traffic tends to be more engaged. But your reach is limited to that subscriber base.
In-Page Push, on the other hand, doesn't require any subscription. The notification-style ad simply appears on the webpage itself while someone is browsing. In my experience, this distinction is the key factor when evaluating iGaming campaigns.
I used to assume a smaller, "warmer" opted-in audience would naturally perform better. What surprised me was how slowly data builds up with Classic Push compared to In-Page the volume just isn't there in the early stages. In-Page tests give you statistical significance much faster since you're getting far more impressions and clicks.
That said, more clicks doesn't mean more deposits or conversions, so I wouldn't judge either format by CTR alone.
My recommendation is you should use In-Page Push for testing GEOs, creatives, devices, and offers. It reaches users you simply can't access through a subscriber-only audience, and gets you data faster. When you want a warmer, more responsive audience, you can try Classic Push.
If you're just starting out, test both formats with a limited budget before committing to one.