Ran some informal side by side tests. The Apple A9 (the one on the cheapie 2017 iPad 5th gen, not the X version on the Pro) was actually noticeably faster than A8X in the tasks I tried:
- displaying PDF pages in GoodReader (technical manuals)
- web page rendering
- launching YouTube app and browsing videos
- searching for text in a 2MB ebook
- launching Excel and loading a (very simple!) spreadsheet
- app installation (Gmail)
Last three was where the gap was most noticeable. I could check email already on the 5th gen before Gmail even finishes installing on the Air 2. Excel took more than 10s to launch on A8X vs 4-5s on A9 and opening spreadsheets and switching tabs was noticeably slower on A8X. Sometimes selecting cells, too.
A8X and A9 are evenly matched when it comes to multi-core. It's single-core where A9 pulls ahead (by ~50% on average, iirc). I think A9 is also when they switched to LPDDR4 and PCI express flash storage (previous gen was eMMC, I believe). Really, there's so many moving parts and more likely than not, performance improvement is a symbiosis of all these upgrades (chipset, memory, storage, networking).
Mind, for iOS 7+ UI eye candy, it was easy enough to pinpoint graphics performance as the culprit at least with the following models.
UI lag (1-worst to 4-best)
- iPad 3 (A5X/1GB, 2048*1536)
- iPad 2 (A5/512MB, 1024*768)
- iPad 4 (A6X/1GB, 2048*1536)
- iPad Air (A7/1GB, 2048*1536)
Same CPU perf on iPad 2 & 3 but 3 was still slower. Same RAM and resolution on iPad 3, 4 & Air.