In a dedicated home theater, where every aspect of movie presentation is at the highest level of accomplishment from sound to image to décor to seating separates rule the roost. When implemented by a knowledgeable installer, who knows how to tune the room as well as the system, separates can dominate a large room with dynamic, and powerful surround sound.
With more room in the chassis for bigger components-power transformer, capacitors, heat sinks-the multichannel amp is a beast unleashed, limited only by household electrical circuits. Meanwhile, the surround processor doesn't have to share a power supply with the amp, and its delicate, low-powered components are safely housed in a separate box. While amplification and surround processor functions can exist in the same product, reconciled by smart circuit design and layout, AVR designers have to live within limitations that are minimized when the amp and surround processor are divorced.
If you don't want your choice of speaker to be limited to what amplifier mettle can be built into a single AVR chassis, separates are the way to go. No matter how demanding your speakers are, regardless of their rated sensitivity/efficiency and impedance, one or more outboard power amps can accommodate them. For the most power-hungry speakers, you may need to look beyond five-to seven-channel amps to a whole rack of stereo or mono-block amps. But where there's a will, separates give you a way.
Ensuring that the speakers have a bountiful supply of power will bring audible benefits. The main one will be freedom from clipping during loud passages, which can drive a lesser amplifier into harsh distortion and may even damage the speakers. The system will be better able to navigate dynamic extremes from a whisper to an earthquake.