Specifications schmefications! I defy normality, for there is no such thing!
Specs are guidelines to give you a rough idea whether using that particular item is practical and sane in your application. I wouldn't throw road-course race brake pads on a street daily driver vehicle. You would have to ride the brakes for a mile to heat them up enough to work. Same reason I wouldn't try to play dubstep on speakers that only go down to 50hz, you wouldn't get the full effect.
Yes, I get that. Specs are a good place to start.
But we also have preferences. I was discussing this with my wife tonight while we were watching TV on the couch, and although she isn't into audio the way I am, she made a clever observation. "If specs were any indicator of preference, there would ultimately be only one set of speakers made that everyone would prefer," she said. "Or, all speakers would sound exactly alike."
Speakers don't sound all alike. Perhaps that is because rooms are different, music is different, playback equipment is different, our ears are different, and we all have different preferences on top of everything else.
So perhaps specs are a great place to start, but as a guide to what's 'good' and what's 'not good'? Not so much.
I truly do not understand the obsession with numbers with regard to audio. No one comes over and measures my picture tube and says I'm watching with the magenta a tad too high, or that my plasma screen is not 'accurate' so it can't be good. I watch it and if I feel like fiddling with it, I do, without regard to what anyone else thinks is proper.
But make it
music instead, and oh **** oh dear everyone has a stick up their butts and they point to lines and graphs and ooh and ahh over things that my messed up ears can't hear anyway; but I'm supposed to conform to someone else's idea of what MUST sound good, because this squiggly line right here says so. Present company excepted, you guys are all being very reasonable, I believe.
To the OP's question - do different speakers sound different with different source material? Yes, many of them do.
To the general thought that even if they do, they shouldn't? Yeah, no.