Each amplifier design has a different output, even those with differing power ratings from the same manufacturer. They have a "sonic signature." Some are "fast," some are "euphonic," some are "bright"... you get my idea. If you send one type of sonic signature to the right channel woofers, for instance, and another type of sonic signature to the right channel mids or tweeters, the speakers response times will differ, making it impossible to acoustically align - unless you can move the individual speaker elements back and forth to compensate for the differences in timing. Listening to such a speaker - especially in nearfield - will produce exaggerated differences in acoustic output, thus making the total overall system response errors greater than the designer imagined. I'm sure that there are others on this list who can explain it better, but to try a test use two different amps on two identical side-by-side speakers. Listen to each (in mono) separately, and see whether you can hear a difference in the speakers. I think most on this list would agree that there probably would be a difference. Swap the amps & speaker leads to be sure it's not affecting your test. If you can define the difference, imagine if each amp were driving a different element within one of your speakers. Think it would affect the sound? Most people who have heard this agree that it can affect the sound we perceive.
I'd appreciate a more scientific opinion if someone has one, since I only base my judgements on what I've heard - and I'm certainly no engineer.