Hey Monster, figured I would reply here since it's sort of a GOTL thing. Sorry for the book you are about to read.
Having listened to them both several times, I could give a vague description of the Tung Sol 6080 vs the 7802, but I haven't done an AB. I'm happy to though, I have both, I'll see if I have time today or tomorrow. Right off the bat though, the difference is large when it comes to soundstage, dynamics, resolution.
They do have a very similar internal construction, only difference I see really is a finer grid on the 7802 and some extra support rods. Maybe shinier copper on the 7802 grid rods? I'm splitting hairs HA!
One thing to keep in mind, the only circuit I have ever seen the Tung Sol 7802 used in with listening impressions is a cathode-follower OTL, like the Bottlehead Crack, Woo Audio WA3, etc. In those circuits, the output tube provides near 0 gain no matter its amplification factor, whereas in the GOTL, The 7802 will operate at a gain of 9 and a transconductance of 20,000 and the 6080 at a gain of 2 and a transconductance of 7,000.
From my reading, the higher transconductance of the 7802 vs 6080 in the Crack(atwoa) cathode-follower circuit will have a negligible effect on the output impedance, so I don't think the better sound can be attributed to that, but I'm still not sure if the higher transconductance is contributing in any way to why the tube sounds so good in a cathode follower or if there is another reason. It's hard to say if comparisons are still 1:1 in the BHC vs GOTL.
I'm very curious myself if it will carry over to the GOTL or not, maybe Glenn can help based on the specs, but I won't know for sure until I have the GOTL!!! When I do, this will be one of the first output tubes I try.