Hi,
basically BGA is not device-dependent and you should run it on any device with browser. But what can have impact is the browser itself you are using. So, instead of buying new tablet immediately, I would try another browser in your current tablet and also you can check if your current browser is up to date.
Also to note, some games are not well fitted to smaller screens, not all games behave the same because they are usually developed by different developers. So try different games, if only some of them have troubles which are blocking you to play on tablet, It is maybe bug and you should report it so the developer can fix/improve it.
Hope it helps
Adam