I have one more theory. Amps differ in their ability to provide current into low impedance and phase shifted loads. The type of amp (class A for example) doesn't tell you how well it provides current. If the speakers in question have an impedance dip in part of the frequency range and one amp provides more current into low impedance loads, the speakers will have a different frequency response between one amp and the other. This difference in frequency response could explain issues like a difference in soundstage.
I've heard a dramatic example of this. I have a pair of Thiel CS6 speakers that dip to around 2 ohms in part of the frequency spectrum. I run them with a Krell KSA 300S that doubles its power down to one ohm (300 watts @ 8 ohms, 2400 watts @ 1 ohm). When I took the amp in for recapping I tried hooking up my Onkyo A/V receiver to the Thiels. The results were laughable. The Onkyo sounded like an AM radio. The soundstage was flat as a pancake. I figured there would be a difference but I had no idea it would be that dramatic.
IMO, many if not most audiophiles do not fully appreciate the impact that speaker impedance curves have on the sound of a particular amplifier. Two amps with identical power at 8 ohms can sound radically different on a given set of speakers depending on the speakers' impedance curve and the ability of the amps to provide current into difficult loads.