I will say that when I had a $500 Kenwood home theater in a box kit 20 or so years ago, the whole thing sounded terrible. I just didn't know it.
Then I got some Def Tech BP30 speakers. I didn't have my new A/V receiver yet, so I hooked up my new speakers (actually a full 5.1 set of DefTechs) to my cheap Kenwood receiver. The sound completely blew me away with how much better it was.
A month or so later, my Yamaha RX-Z1 came in. This was a $3,000 A/V receiver, so I was all set for just how much more amazing things would sound.
Answer: Not at all different.
Yes, the new receiver could play louder, for longer, without issue, but at normal listening levels, the Kenwood and the Yamaha sounded quite similar. The Yamaha had all the fancy surround modes, and actually supported audio formats the Kenwood didn't, but as far as actual sound... It just sounded the same.
The speakers, by far, made the biggest improvement to our listening environment.
That's about as real world as I can get on this.
An outboard amplifier will give you plenty of power, if you need it. If you crank your speakers all the time, then it will support that sound for hours on end, but if you don't crank it up, then the Pioneer's amp section will do just fine. Either way, sound should be the same at normal listening levels.