According the S5 & S6 GSM Arena battery results, the 14nm didn't much to improve the S6 either actually with a 11% decrease in overall score. And I saw a recent review of the S6 and the reviewer wasn't impressed by it saying it sips battery juice faster than the S5. I think some of the issues is Samsung went 2K instead of sticking to FHD and lowering the battery capacity to keep it thin. I believe 2K should only be for devices above 5.5" or tablets and need to pack a minimum of 4000 mAh.
Fortunately, Apple avoids the stupid race for increased resolutions and high ppi screens which aren't efficient or even noticeable for screens under 5.5". Whether they go 14nm with the A9 but increasing clock speeds on both CPU and GPU might still result in a stalemate with battery life. Looking at the s model track record, I really doubt of any substantial gains. Just be grateful Apple may double the RAM this year.
14nm doesn't tell the whole story. If you did a simple die shrink and stuck the new chip into the S5, then you'd likely see a sizable increase in battery life if everything else remains constant.
But, the S6 also increased the pixel density, decreased the size of the battery, increased the RAM, and went to an octa-core processor (lower clock speeds in a big.LITTLE configuration). Individually, every one of these items potentially decreases the battery life. Added together, they negated whatever power savings came from the die shrink.
Consider that the A8 cut the power consumption from the processor in half, and the vast majority of this reduction came from the 28nm to 20nm die shrink. Apple made the tradeoff on battery life, because it went to a larger and higher resolution screen. They also increased the battery size, and in the end, the 6/6 Plus did increase the battery life compared to the 5/5s.
Also, the A9 likely will entail more than just a die shrink. The A8 had minor architectural changes compared to the A7, so Apple is due for a more substantial revision. Since the screen size and resolution likely won't change on the "6s" the likely outcome will be huge leaps in performance, battery life, or a combination of the two.
As I indicated earlier, I suspect that Apple will hold the battery life constant, and allocate all of the efficiency gains towards greater performance.