i wouldn't call it tone so much as feel. the frequencies (i hear) seem to remain the same. a quick test could be if you set the amp to whatever then switch back and forth the power switch setting (putting it in standby between switching, of course).
the full power setting should be louder, but not too much different tonally. you definitely lose a bit of the headroom, especially at lower master volume settings, but maybe you're going for the raspier clipping (variac + tweed power in 10w mode, high gain, high mids, high master is pretty awesome). low end needs more power to be felt/heard by a normal human ear, so maybe that is the "tone" that you sense is changing. full power is definitely more "immediate" in response to pick attack, bass-heavy chording, etc. sometimes i feel like i have to fight more for legato fluidity when not in full power. idk if anyone else feels this way...
in an ideal world, the tone would not change by just adjusting the power setting, but it can for some. it doesn't much for me either, so i'm with you hendog.