JohninKansas point about the tempered versus the untempered scales is still important, since, ewven now, only keyboards and fretted instruments are really tempered(and fretted instruments can be tuned with perfect chords in open positions and tunings) --violins/fiddles always play the perfect fifths rather than the tempered ones, and the D penny whistles and such are usually not tempered--

In addition, even when part of a tempered scale, different key notes have different sounds, partly because the audible frequency range is fixed, and the higher the note, the fewer audible overtones it has, the lower the pitch, the more audible overtones, and partly because the instrument(even the voice) resonates differently relative to different pitches(guitarists know that a D down tuning makes the instrument vibrate in a whole new way)--

So different songs played in different keys do sound different--if they didn't, what point would there be in having different keys?