For the sake of getting my hopes/expectations written out, I'm expecting a bigger performance jump for the A9 vs the A8 compared to the A8 vs A7. Part of it is assuming that "S" iPhone refreshes are still focused on speed and part of it based on evidence in the developer previews that the next iPad Mini will include full multitasking support including Split View which I presume will mean the use of an A9 with performance similar to the A8X. Apple promoted the A8 vs A7 as having a up to 25% CPU and up to 50% faster GPU and I'm expecting a 50% faster CPU and 2x faster GPU in the A9 vs the A8.
I'm still expecting a dual core and the CPU performance gains would come from both clock speeds, perhaps 1.6-1.8 GHz, and architectural improvements. At WWDC this year Apple introduced Bitcode allowing apps to be stored as LLVM intermediates on Apple's servers so that they can always be compiled with the latest compiler on distribution to users. They said one of the motivations for this is to allow apps to automatically take advantage of new processor capabilities they might be adding. I suppose that want to avoid the flip-flop situation where the armv7s target for Swift (A6/A6X) was added as and then later removed as a default target in Xcode. Seeing Apple is making all iOS 9 apps use Bitcode by default the A9 may well come with an evolved ISA and bigger microarchitecture changes (relative to Typhoon vs Cyclone although I'm not expecting a complete redesign), perhaps armv8.1 which ARM said would see silicon by early adopters later in 2015 or maybe Apple's own set of customizations.
For the GPU, I'm expecting a PowerVR GT7600. A more aggressive 6 cluster configuration vs a 4 cluster configuration better suits the iPad Mini 4 and would also give a useful performance boost on a per pixel basis for the iPhone which didn't see much improvement in the iPhone 6/6 Plus generation due to the increased resolution.
Memory will hopefully be 2 GB LPDDR4, which is probably the most important requirement for Split View in the iPad Mini 4. It would be interesting to see an increase in the L3 cache if it'll allow them to more aggressively power down the memory controller.
For the A9X, I'm expecting a 1.8-2.0 GHz tri-core CPU with a 2 x GT7600 implementation. Higher clocked in the iPad Pro and lower clocked in the iPad Air 3. Perhaps 4 GB of memory in the iPad Pro and 2 GB of memory in the iPad Air 3.
https://www.semiwiki.com/forum/content/4824-tsmc-apple-update-q2-2015-a.html
If Semi-Wiki is to be believed, that the A9 will be Samsung 14 nm and TSMC will get the A9X on 16 nm FF+, then I'd think there must be an iPad Air 3 in order to justify the volumes to not only make a A9X, but put it on a different process, since an iPad Pro isn't likely to do it alone and there's no indication that the new Apple TV will use the A9X even though it's supposed to be gaming focused. Given the lack of iPad Air 3 rumours, perhaps it'll just be a low-key refresh like the iPad Mini 3, in this case with just an SoC update, or perhaps it'll launch in spring 2016 as an addendum to the inevitable Apple Watch update.
As to the rumours above of higher resolution screens for both iPhones, I hope Apple isn't going to play the dpi game and waste GPU performance driving higher resolution screens that don't provide much user benefit. I don't believe there have been many complaints about the 401 dpi iPhone 6 Plus screen and working from 3x graphics before scaling down seems to have alleviated issues from non-native scaling. I could see them switching to 3x graphics scaling and 401 dpi displays in the iPhone 7 if only to simplify their supply chain, but native 3x displays in the iPhone 7 and 7 Plus seems like a waste.