I think it's the complete opposite, actually. Maiden changing their production, acquiring Bruce and so on did give them some of the "cleaner" sheen and moved their sound from "hard rock"-adjacent do outright "metal", but if anything, they leaned into their idiosyncracies - the ever-present love 'Arry always had for prog and art rock and the general high-brow attitude became only more prominent with time (and more obvious with the clean production and Bruce's soaring vocals) and Maiden post-TNOTB were
more unique than they were before; they actually managed to leave all of their NWOBHM brethren far behind.
On the contrary, Priest moved from quite a bit of an idiosyncratic, experimental and downright
emotional band, dumbing it down, becoming more stereotypical and predictable in the process. The juiciness was lost, the metal streamlining did sometimes work (
Defenders, about a half of
Screaming), but the true creativity kinda took a nosedive.
Even with Prodigal Son/Remember Tomorrow/Strange World, which are some of the biggest outliers in Maiden's early career, I can see the latter versions of the band doing something like that - after all, they always had the tendency to throw the occasional spitball; Still Life, The Prophecy, Isle of Avalon, Journeyman... But I can't imagine post 1979 Priest covering Joan Baez or Spooky Tooth. Heck, I don't even remember something similar to that funny Exciter's "
Pet Shop Boys section" on the latter albums (though correct me if I'm wrong in that regard).
To me, with the unification and the homogenisation of the sound, Maiden only became more Maiden, whereas Priest became more "metal". If that is a prime example of a double standard, in that classic
"quod licet Iovi, non licet bovi" way, so be it.