The features alone make the galaxy s 4 the best phone.
Faster processor, more features, replaceable battery, bigger screen, better camera in great light, 4.2 (why the heck is 4.1 still coming out on any new phones?), swift key included, storage expandable by up to an additional 64gb. in terms of functionality (which is why I buy a phone) the s4 takes it and that's fact, not opinion.
It most certainly is opinion. While the S4 may be the most functional phone for how you use a phone it wouldn't be for me.
Here is how your positives of that make the S4 better for your use don't apply to me at all:
1. Marginally faster processor. Will not be noticeable in real world use.
2. More features. Most of which will never be used after the first couple days. While not a negative, certainly not a positive either. Quality, not quantity. I'll take Zoes, Highlight videos, and blink feed that I like and use over S-Health, Air View, the air gestures S-Voice, S-Translate, and all the other S4 features that I won't use.
3. In the past 10 years I have never once purchased an extra battery for my phone. So while a feature to some, I truthfully do not care.
4. Bigger screen. I can barely use my One one handed. The width of the S4 would make this more difficult. For me one handed use is a bigger feature than screen size.
5. Better camera in great light. Okay, most of my photos are in my poorly lit apartment of my 1 year old daughter. The One's superior low light and indoor camera make it the better camera for me
6. 4.1 vs. 4.2. What exactly are we missing? Both the phones are so heavily customized that none of the 4.2 features even matter.
7. I personally prefer swype to swiftkey. Doesn't make either of us wrong. I was using Swype on the Note I had before this.
8. I have never needed more than 32 GB (Note was 16 with a 16 SD card). So since the base One is 32 GB, no issues for me.
So for me the One wins in terms of functionality.
I'm not saying your opinions are wrong, just your statement that it is an objective fact that the S4 is more functional. All your points may certainly be valid for you and make the S4 the better phone for you, but that does not make it objectively better. I wouldn't say either phone is objectively better than the other. It is a matter of what matters to each individual.