Unreasonable Rant Mode On (and nothing against you Corey, I love you, man):
Since the Tone King has generally proven himself to know absolutely
nothing about guitar tone, based on his demos, I'll pass. The man has the worst tone I've ever heard from anyone purporting to be a guitar gear expert. Ever. But that's just my opinion. Feel free to disagree.
And who's the guest -- Riff City Guitar? Hmmm...I wonder what they're going to try to sell...
The truth about tubes? It's like anything else guitar tone related:
Some sound good, some don't. And not everyone will agree on whether what they hear is, or isn't, good. There is no objectivity in tone - the Tone King is living proof that people have different ideas about what good tone is - it's personal. It's subjective. Some folks can't even hear differences at all (my wife, for example thinks all electric guitars sound alike*).
The classic old tubes -- Telefunken, Siemens, RCA, GE, Mullard, Brimar, Bugle Boy, Philips, old Tung-Sol, etc., etc., actually
do sound better
in some amps depending on the design of the amp, and
actually do have a lower failure rate. No myths.
And some amps depending on the design do just fine with newer tubes, and NOS might be a waste.
Since people will never agree on what sounds best with what, it's utter nonsense to expect to have some hushed up secret mythology suddenly outed by some 'expert' dude.
I've done a lot of experimenting with tubes in 25 years in my studio, and I hope my clips have shown that I have at least a minimal understanding of how to get good tone from my rig.
I've used the NOS tubes listed above and there is a difference that is audible and repeatable. Doesn't mean better, or worse, in all applications, though.
There are no rules! Lots of players comparing new and old tubes might prefer the new tubes. And they'd be right as rain - for their needs.
The only way to know if your amp will or will not sound better with NOS (or any other) tubes is to try a set in your amp. Listening to anything but what your own ears tell you is just useless babble (including my useless babble, of course!).
I always recommend that people be hands-on and reach their own conclusions, and not simply go with some self-appointed expert dude's opinion when it comes to something as subjective as tone.
This isn't math. It isn't science. It's something far more subjective. Be your own expert. Try stuff out and see what works for you.
End unreasonable rant mode. 
* Example conversation:
"Listen to this guitar, hon!"
"It sounds like a guitar."
"Yes, that is because it is a guitar. But doesn't it sound great?"
"It sounds like a guitar to me."
"But listen to this sound." (SFX: pickup switch click)
"Yeah. I can't tell the difference."