Ok, I'll throw my 2 cents here. I'm using a JJ ECC803S w/ gold pins as a phase inverter in my Copland CTA-504. This is an excellent PI tube, excellent bass, lively but not bright, a sweet sounding tube. The amp came with it when I bought it used. From what I read, swapping PI tubes does not need a rebiasing of the output tubes. So I swapped it with a vintage RCA gray long plates, I believe this was made in the 50s. The sound became lifeless and distant. Wow, I wasn't expecting that. So I immediately swapped back the ECC803S. The lively sound returned. I happen to have 4 more ECC803S so I swapped one with the one I'm using. Stage became a little narrower and not as lively. Hmm, interesting. Tube manufacturing variance? So a PI tube, to me at least, does affect the sound.
I have another vintage tube amp, an Audio Research D-70 MkII. It has a vintage RCA 12AX7A for a PI. This tube is not as sweet sounding. I swapped it with my fav PI tube. Same effect, the sound became livelier.
So if you have a push-pull tube amp, try rolling the PI tube. Its cheaper than rolling the output tubes since it is only a single tube.