This is my exact situation right now. I have to two heavyweight champions sitting on my lap and I'm freaking torn in two. I have to return one and I have no idea which one to return! I love everything about the one except for the camera or
OS - Draw (4.1 or 4.2 don't seem to drastically different to me)
Storage - One
Camera - S4
Form factor - One
Battery - S4
Sound - One
Overall fluidity - One
Intangibles (software) - S4
Decisions... decisions
Its a really tough decision in the end it was the stock elements of Touchwiz that made me go for the One. (The elements I couldn't change with a launcher - or without rooting and rom'in) The dialler is in your face tacky, the people / contacts app is less refined, calculator with its rounded buttons is 10 years out of date aesthetically, and the music app is just not a patch on HTC's tbh, no artist / album gracenote features, no virtualiser, no lyrics option etc... S-calendar is nice alright but gets very cluttered. But worst for me was that each of all these elements had no overall aesthetic coherence with each other, it is like each element of Touchwiz is designed by a different design team so it doesn't flow or feel natural or as one as it should be.
Sound quality listening to the two devices via headphones the One with beats does ave tangible better sound. As I like to listen to music whilst I'm walking that was another consideration too. But not a major one, just one I noticed when the two were side by side playing same music through same headphones. The HTC One produced more detail in the track.
[I am meant to be in charge not my phone] I also felt like the S4 was making me be a slave to memory management, to constantly strive and make my device as smooth as I want it to be (as it should be) and I did not want android OCD. The one is so smooth out of the box and memory management just isn't a concern on the one either.
For me personally battery life was actually poorer on the S4. I could still get through a day before it was put on charge however - but it did seem heavier on the old juice and I'm only in a 3G area (no LTE).
When I added all those things up - for me the tangible benefit of the camera was just not enough compensation for all the other elements that I would use everyday and simply took for granted on the htc one. Things that I did not have to think about such as micro stutters on the S4 only were an issue because I had used the htc one which didn't suffer from them at all.
I want a phone to work for me, not me work for my phone, and the S4 was making me work for it....
I thought to myself, look yes I love the S4's camera - but a camera is maybe 5-10% of a phones usage for me. 3rd party other apps maybe 20-30% of what I use the phone for, but the biggest share is the phones core - the phones GUI and other stock apps make up the lion share 60-65% and therefore they had to be more important for me overall, and for that reason I choose the device that had a better overall design aesthetic and coherency running through its core applications. HTC Note, task, music, calculator, dialler, people, weather, TV, clock etc.. The keyboard on the One is also lovely and as good as swiftkey / Swype alternatives and it keeps the same GUI consistency.
So that's what swung it for me. I am a graphic designer and illustrator by profession, so design coherence is important to me, and looking at a phones basic stock elements that all had an opposite design ethos to everything I was thought and practice for the last 18 years was just too much to ask of me with the Galaxy S4. So for that reason Touchwiz for me is simply a no-go zone, and likely something I won't be revisiting again in the conceivable future.
I don't envy your decision, but at least you can rest assured you have perhaps the best two android smartphones to choose from whichever you opt for in the end.
The S4 is a fab phone, just not the right one for me. But I'm sure for millions it'll be a great fit. As it stands and with the camera improvements on the one - je ne regrette rien.