Irradiance at every point of the receiver is smaller for the angled configuration. The solid angle covered by the emitter is the same, but in the case of irradiance you are not free to choose the normal
I do not understand exactly what you mean by this. Could you elaborate a bit?
The way I thought about it: imagine a hemisphere around the receiver center point's normal. In the first configuration, the emitting surface would be close to the Zenith of this hemisphere. In the second configuration, the surface would be closer to the Azimuth and thus the cosinus factor would be different.