Here is where you are a bit off, the S4 has a 2600mah REMOVABLE battery, bigger than the HTC ONE 2300mah non removable battery, also you do know that MaH batteries can go bad, in the S4 you can just swap it out, what do you do when that happens on the HTC One, they also lose their charging power, I like to have more options when purchasing similar device. Also the S4 is clocked at 1.9 Ghz while the One is at 1.7 ghz with the same processor, the S4 has a bigger screen, and expandeable storage "yes I do use a 64 gig Micro SD card to keep my high resolution music and high resolution movies on, and it is already filled to 55 gigs", how and where can I do this on the ONE, so already I mentioned four options that the ONE does NOT have, so again, why should I purchase the ONE, and last but not least, HTC is horrid with software updates, the flagship HTC One came to market with 4.1.2 while the S4 came to market with 4.2.2, and we all know that the ONE will not see 4.3 till middle of next year, if ever, the way HTC has been with their software updates.
I have owned HTC devices before they THOUGHT they where Apple and crapped on their customers.
One more thing, you are comparing the HTC one battery to the S3 battery, the S3 is an older device and still kicks ass, also the S3 I can change the battery whenever I please, you lost me when you mentioned S3.