I'm going to disagree here. Both draw the same filament current at the same voltage. In the Crack circuit, both draw the same current from the high voltage supply.
If the plate/heater voltages go up with a 6080, then the 6AS7 would in fact run hotter.
In any case, they carry the same ratings and often have the same guts, just in different glass envelopes.
That's exactly what I had in mind at the very start but upon power up I noticed the 6080 got hotter faster and measuring the different pins shows a large difference almost double. I think it might be a shorted tube unsure at the moment because I've been using this pair of 6080 for every 6AS7 amp (not 6SN7 if I mentioned it typo) to test with. But the odd thing is it sounds fine and I get no arc's upon power up. What's the max voltage for the plate of the 6080? 300volts or something 6as7 is 250v max, there is a regulated cap that feeds pin 5 of the socket rated at 250v when using 6as7's plate voltage is 126v but as soon as the 6080 goes in 276vdc, or is the voltage doubled off the positive lead of the cap feeding back to pin 5 on the socket? Otherwise I'd expect the 250v cap to start smoking since it's 26vdc over it's rating. This is not the Crack btw.