Experience: In most amps I've played, output tube changes made little-to-no difference in the sound of the amp.
Guess: Since it's the last thing before the OT/speaker, it takes a very big difference in outputt ube operation to hear an audible change at the speaker. Also, if the amp uses negative feedback around the output stage, that feedback is reducing apparent differences between tubes (but also differences in the same tube over its lifespan).
Disclaimer: I'll admit not spending a *lot* of time with each swap evaluating subtle differences in the distortion, or over the whole range of distorted sounds from a given amp. But to be honest, without recording each setup, I'm not sure how good my (or anyone's) audio memory would be after a swap and rebias to the same conditions.
Result: I have a big stash of old production tubes, but I've never been afraid to pop in a tube from any other manufacturer, new or old. Maybe I'll revisit some testing now that I have some recording toys.
Experience: In most every amp, I've found swapping the input preamp tube to have the biggest effect on the tone of the amp, as far as tube-changes go. I've heard lessening effect as I move down the preamp signal chain towards the phase inverter/output tubes.
Guess: Even a small change at the input tube makes a big overall change, because that small change gets amplified by everything else in the signal path. Also, same caveat regarding feedback applies; if the preamp stage has a significant degree of feedback, there probably won't be an obvious tonal change either intially or during life.
Disclaimer: I haven't spent a lot of time evaluating new-production tubes because I have a bunch of old production preamp tubes and don't tend to swap. That said, I did once buy 5-6 different brands of 12AX7's in one sitting to do a shootout; unfortunately I never really spent the time to do it, and again, without recordings how can you distinguish the likely small differences?
Result: I do generally stick with old-production tubes (true "NOS" is a different thing and almost not seen anymore; when the last time you walked into an electronics store and bought their old assortment of tubes cause they needed to clear room for their cell phones and batteries?). I find that even for exotic "NOS" tubes, if you keep your eyes open, you'll find a good deal on them, while possibly paying as little as you would for a new chinese tube. I think it's worth spending money on these, costs less than exotic output tubes, but is not money-well-spent in necessarily every tube socket.