This might sound "extra", but I think I have a tube/headphone pairing. I am mad at myself for being so picky, but it's the truth.
I have an (alleged) pair of Shuguang Treasure CV181 tubes that I love with speakers or with my HE-6SE, but cannot stand with any other set. Almost sold my HEDDphone over it. The tubes are too damn noisy, with a maddening hum and all sorts of cheeps and chirps, on pretty much everything, but they're not particularly bad with the HE-6SE or my speaker setup.
That, and while the tubes have incredible soundstage and detailing, I find them a little hard sounding in the upper mids which actually works in the favour of the HE-6SE. On everything else, I love my orange-label Sylvania 6SN7GTB. Low noise, not harsh at all, good bass presence, liquid mids. Perhaps lacking air and are not the last word in detail, but I'd trade a hint of air for a lack of fatigue any day of the week.