I'll leave the gospel to people more worthy, but will lodge my ever faithful vote for the benefit of Pixie Dust - i.e., that better sound from more powerful amps.
One: it is not at all like religion. I don't believe my pro amp sounds better than my Denon. I think that because when I listen i don't hear evidence of clipping well before the scientific db levels say they should be there. In other words, it sounds better. I can A.....B, and do (but it takes some time) and clearly notice cymbalance and other small issues from my Denon on certain notes. That's not faith, that's just a lifetime of trusting my God given senses.
Two: volume is key. JohnK like his music lower than mine. I like to feel music, horns, drums, acoustic guitar, whatever. I get that at around 100db, with spikes well above that (hello 108). The rubber meets the road on this issue when John's A/B testers are treated to music that requires lots of power to meet a peak. Then the $12 JVC does not keep up with the Bryston.
Don't trust me, read Alan's technical articles. Music can easily defeat your Onkyo trying to hit certain notes at certain volumes. Axiom does not do a lot of posturing, and I doubt they would invest the R&D time to develop a 1400 watt amp if a $50 Sony would do just fine.
My pro amp rolls along without issue because it has over 500 watts and defeats the Law of Diminishing Returns because I got it for $500. So I keep the 10 year old Denon and get the power I wanted. Saved $1500 on a new AVR.
In short, JohnK is right, and you should buy a separate amp.