I'm not certain any of the 9MM advocates intend to compare ONE shot of 9MM vs ONE shot of .45. I think the intent is to compare 2 shots of 9MM to one shot of .45 (or 3 shots of 9MM to 2 shots of .45 based on effective recoil recovery). Whatever the ratio was meant to me it was not meant to be 1:1.
I think the FBI's statement, taken at face value, implies that they believe there is a 1:1 parity in terms of practical effects in real-world shootings.
While the 9mm was benefitting from modernization, so were other calibers. Currently the modern .40 loads are equal to or surpass the .45 in a platform that can carry 16 rounds.
It's all getting better. As far as I can tell, that doesn't mean that they all perform more similarly than they used to, or more differently either, for that matter.
The improvement in ammo design/performance is a red herring, IMO. When the FBI originally chose the 10mm and then the .40, they did so based on wound volume calculations, not based on definitive results from real-world shootings. In other words, they switched to 10mm/.40 based on differences detected in a parameter/calculation that no one has ever been able to definitively show has a practically significant effect in real-world shootings. They did that for two reasons: First of all, because someone sold them on the idea that the parameter/calculation was telling them something important. Second, because they had to have some reasonably defensible selection criterion.
I'm sure at the time they believed that the performance of their new caliber would, over time, prove that their artificial selection criterion was valid. Instead, after nearly 30 years of trying to prove that their decision was a good one so that they could justify the extra training costs, lower capacity, poorer shootability, etc. they finally had to admit that neither they, nor anyone else, has been able to do so.
Rather than admit that they made a mistake, they tried to explain that ammo design has improved enough that 9mm now performs as well as .40. It's pretty easy to see that explanation doesn't really wash. Any technology improvements bringing benefits to the 9mm should also benefit the .40 as well and the .40 should improve in performance at the same rate, if not faster due to having additional momentum/energy for the designers to play with.
The reality is that the practically significant difference in real-world fight-stopping performance wasn't there in the first place and they've finally been forced to that conclusion after trying and failing to prove its existence for decades
It's not that the difference has gone away due to ammo design advances--it wasn't ever there to begin with. This shouldn't be a surprise to anyone who read Urey Patrick's paper on handgun wounding and effectiveness. He admitted in 1989 that the terminal performance differences due to caliber selection (in the context of service pistol calibers) made so little difference in the real world that it wouldn't be possible to detect it without examining huge numbers of real-world shootings. He was just more right than he realized.
They've been looking at the outcomes of real-world shootings for another quarter of a century since his paper was released and they still haven't been able to show enough of a difference to justify going above 9mm. Neither has anyone else, for that matter.