This is very disappointing if true. There's only so much optimization of the SoC a company can do to save the battery life. An LCD screen is an LCD screen and the bigger one rumored for the new iPhone will definitely use more battery than the screen in the 5S. An 1810 mAh battery is just pathetic compared to other Android phones with similar screen sizes. The Moto X (4.7" @ 720*1280) has a 2200 mAh. The Nexus 4 with 4.7" @ 768*1280 runs a 2100 mAh.
Yes, Android tends to be worse than iOS in terms of power efficiency but with a bit of mindfulness, I run my Galaxy S4 for two days on a single (85-90%) charge while my brother's 5S never late more than a day with similar usage patterns.
Apple needs to step it up. I really want to switch back to iOS with the 6 (I left after owning a 4S for a year due to small screen) but if they fail to deliver a phone with mediocre battery luge, then I'm sadly going to have to stick with Android for at least another year. And I really don't want to do that.