The specs published utilizes a resistive load and there are no speakers that present a resistive load, so when you combine the complex load of a speaker, the frequency curve of an amp will not be as flat anymore.... whether it's this that may make differences or actual compression due to the fact that some speakers require the amp to provide quite significent current loads.... I don't know....
There are many other things like TIM and phase response ans others....
I know there's a story about a guy working at Adyton in Norway doing the fine tuning of amplifiers by ear, because the measuring instuments was not fine tuned enough to get it 100% right....
Whether this is fact or fiction, I have no idea, but it's an amusing story
A higher bandwidth will make the phase response more linear within the 20KHz bandwidth, you need very very wide bandwidth to get linear phase response up to 20KHz. Whether this makes a difference or not.... I have no idea
There's much more than frequency response and thd that may make a difference, I think......