You're asking about the difference between separates (preamp+amp) and receivers.
A preamp(+ amp) usually costs more than the equivalent receiver simply because of manufacturing economies of scale. Receivers are sold in large quantities. Preamp/processors are not.
The reasons people buy preamp/processors usually have little or nothing to do with the resulting audio quality. Modern high-quality receivers have distortion levels far below what can be heard. So far as I'm concerned, most of the reasons for choosing a pre/pro are emotional, and some of them are rationalizations.
I prefer a preamp+separate multichannel amp because of the potential improvement in reliability, and perhaps in the quality of the design. In my case, the pre/pro is the same size as the equivalent receiver would have been, but it contains far fewer circuit boards, so there's better convection, so the circuits can run cooler. Since it does not contain the amplifier channels, it produces that much less heat to begin with. The quality of build doesn't directly contribute to the quality of the sound, but, again, should contribute to the reliability of the electronics. Similarly, the multichannel amp that I use is itself the same size as the receiver would have been. It has a much larger power supply, though, so it should be better able to provide the output power that it's rated for on all channels simultaneously. Like the pre/pro, it also doesn't have additional circuitry which would be contributing to the heat and reducing air flow.
FWIW, even after long periods of activity, both units become only somewhat warm to the touch.