Alright I'll take at shot at answering your question.
C2 does 1080p. This is not the limit of the engine. This is just pixel(w/h) value. C2 will do just fine, but it's not your entire answer regarding what you want. If you were running on the PC you would be just fine. your not. Your targeting mobile platforms I suspect Ouya and iPad with retina?
"Almost all modern platforms hardware-accelerate rendering. Construct 2 does not have any particular weakness here; if the hardware can handle 1080p rendering, then I'm sure Construct 2 games will work OK as well."
This is true to a large extent, but not everything. C2 piggy backs on UIWebview(built in browser widget for ios and android). This for mobile has hit major rendering road block. WebGL is the javascript bindings to the OpenGL graphics acceleration. Which IOS and Android do not have. It only has canvas acceleration and it's not the same thing nor does it carry the same rendering speeds. In fact Canvas acceleration is much slower than any of the GL rendering.
The Tegra 3(Ouya) can in 720p in OpenGL ES can render 5000 moving sprites and get smooth performance. In the Android NDK(Java) youtube.com/watch A simlar test on PC in C2 with WebGl and I only managed 3000 in 720p before the 60fps would slow down. The same test on the iPad2 resulted in a steady 80fps before slow down. The tegra 2 resulted in 15fps(browser and CocoonJS) for only 10 sprites. Now these aren't the Tegra 3 which will do better. ok cocoonjs
CocoonJS is a canvas accelerator. It attempts to improve logic performance to native speeds. It improves Canvas rendering by a lot too. It does improve performance for for IOS and Android. Doubles the base FPS, but will quickly drop down based on a sprite curve. ie the more sprites the more the performance curve drops. The catch here is that CocoonJS/team Ludie doesn't have an Ouya and CocoonJs apps crash. So there is no option to develop for Ouya with CocoonJS. Your limited to using Phonegap and performance is nowhere near as good.
For now. Skip the 1080/960. Go for 960x640 and keep the sprites down for now. Until coocoonjs is workign anyways.
good luck. C2 is awesome :) buy it