Quad, particularly next-gen quad such as the S4 Pro, next Exynos and any A15-based designs will be helpful to drive the 1080p resolutions. People forget that you need processing power to push out those extra pixels.
Pushing out those extra pixels on 1080p displays is something only the GPU is concerned with, so you are absolutely correct that the quad-core S4 Pro would be most welcome in that regard, but only due to its much more powerful GPU. In comparison to the GPU, those two extra CPU cores are practically worthless for this purpose. Whether or not a CPU design is A15 based is also irrelevant, as that only refers to the CPU architecture which is barely involved in pixel pushing.
Based on that, the 820 and 8S should
theoretically perform much better than the HD devices.
They will. No way they wont. In games you will see significantly better performance with the low res screens than the 720P screens. Unless the game is changing the resolution on the device which I do not even know if that is possible in the API.
You were both quite smart in how you worded those statements, using the words "theoretically" and "unless"
In fact, Power5 got it exactly right, as it just so happens that "changing the resolution" is exactly what most games do (more relevant for fast 3D games like hydro-thunder than a simple tic-tac-toe game).
Of course, the resolution of a device's display never actually changes. Instead, games simply render their content at much lower resolutions. Virtually all fast-paced/highly animated/3D games render their frames at half WVGA resolutions (i.e. 400x240 pixels). On WP7 games often used even lower resolutions, but I don't expect games to go any lower on WP8. Up-scaling to the devices physical display resolution is done by a hardware scaler, and is therefore computationally "free of charge".
Thanks to this functionality, game developers can choose to lower rendering resolution in exchange for higher frame rates and vice verse, which gives them more flexibility to tune their graphics engines. This also allows developers to target a single resolution, independent of the varying physical display resolutions that may exist, and that is exactly what developers are doing.
Because every high-performance game will determine its own sub-WVGA rendering resolution, which is likely to be very similar (if not identical) across all handsets, it is safe to expect games to perform almost identically, independent of varying physical display resolution. That includes WVGA devices like the 820 and the 8S. This ensures all customers get identical frame rates and a consistently good gaming experience across all devices. I think that is a pretty awesome feature.
I couldn't find anything simple to back this up with, but Microsoft has documented the feature in the WP7 and
WP8 SDK (see DXGI_SWAP_CHAIN_DESC1.Scaling)