I wouldn't say H2H do not improve *at all*, but I *would* say that you wouldn't be able to use your "by a fair margin" clause for H2H. In its case it's really only by a relatively narrow margin.
Is that bolded part *not* a change to strategy? At least insofar as FFXI *has* changes to strategy? (Because practically every fight in this game boils down to "tank and spank with some optional crowd control".)
Perhaps "change strategy" isn't quite the right term... but Aegis/Gjallarhorn do make fights significantly safer and easier with bigger margin for error (or unexpected problems that aren't anyone's error). A tank who's that much harder to kill? MP users with that much more MP to burn?
So yeah, I wouldn't say it changes the original strategy, but it certainly makes it much easier to execute, or makes it possible to execute it with fewer numbers. In a different way from simply having a little bit more damage output (which makes for the same *difficulty* of the fight while it's going on, but a slightly shorter fight).
And Kirin's not exactly a good example, seeing as he can just be TP-burned to death without relics or indeed without anything resembling a strategy other than "kill fast".