This is true for me. The microarchitecture and clockspeed difference between Air 2 and Pro 9.7 is impressive. Sure, if benching the tri-core A8X and dual-core A9X, there are some tests where they're neck and neck. However, most apps are dual-threaded at most (optimizing for more threads is not always feasible) so from a real-world perspective, the Pro 9.7 gives a significant boost.
I know a lot of folks have complained about the Pro 9.7 being "RAM-starved". Honestly, having used an iPad 4 (A6X) and iPad Air (A7) both of which have 1GB RAM on iOS 8 to 9, I'd take "RAM-starved" with faster CPU anytime.
Of course, I realize whether the extra performance boost is worth it or not is all dependent on price point. I wanted 256GB so the Pro 9.7 was the only option and at $1029 (LTE), I found the pricing acceptable if not ideal so for me, it was a no-brainer. If Apple had priced it higher, say $1500, I definitely would've gone with a refurb 128GB Air 2 for ~$700 with tax, instead.
For older CPUs (pre-A6), not really. The old CPUs were pretty much just barely good enough to run the mobile OSes at release and a major firmware upgrade with some performance penalty. Beyond that and you get significant slowdown.
The A6 on iPhones have aged quite gracefully and even now, I'm pleasantly surprised with iOS 10 performance on my iPhone 5s (A7). Alas, the bar is higher for the iPad, particularly when you go past iOS 6.