One could argue the X20 could have lower power consumption because it's actually a 3-module "big.LITTLE.LITTLER" arrangement and it's done using 20nm (unlike S650's old 28nm), but turns out the Note 3 S650 has longer battery life.
Compared to it's predecessor a X20 smartphone hasn't that much more battery life, if any. They just run notably cooler. On the side it's actually good to see QCOM catching up again especially in sales.
That said Kishonti has now a quite demanding GPU bound battery life estimating benchmark running Manhattan 3.1; what I'd also want to see on top of that are temperatures at the end of the 30 loops of the benchmark. It's not like SoCs haven't any temperature sensors to reveal numbers, it's just that probably no one thought so far it's necessary. It doesn't do me any good if after a torture benchmark N SoCs isn't throttling by a worthwhile margin, but the device gets too hot to even hold. That has nothing to do with the SoCs mentioned here, but it has happened in other cases.
Oh and last but not least: 20SoC has the problem that it's not really preserving enough power to really justify the investment compared to 28HPm: http://images.anandtech.com/doci/9762/P1030606.jpg?_ga=1.32351228.334006868.1458215934