[Hinrik]

>I'm not sure what you mean by "sound the same", but just by comparing a simple change from major to minor is quite a dramatic change

That's because OP is not talking about the differences between scales (major vs minor) but keys (C major vs A major). With equal temperament all keys of the same scale have the exact same intervals between the notes. They are simply shifted up or down by a constant amount. Before equal temperament that was not the case.