As with any user comparison, the views and thoughts are purely subjective. I don't pass this off as fact. This comparison is based off of MY own experiences with both. Both devices are with AT&T. I owned the One and currently own the S4.
HARDWARE
Well, the forums are alive with the debate over who has the better hardware. I must say that I was truly enamored with the aesthetics of the One. It is narrow enough to fit in the hand well. The curved back also adds to this feeling. The phone still feels light even with the aluminum build. BoomSound is phenomenal. Sound is nice and full. Button placement was horrible for me. The power button is too recessed and I didn't like the capacitive buttons. This doesn't mean they're not functional; I just didn't like it. The S4 is sexy for what it brings to the table. I prefer not using a case and the soft rounded edges of the plastic feels better in my hand. The button placement works better for me as I don't have to adjust my hand once I turn on the screen or to use it. The sound cannot compete with the One. If I had my choice, I would prefer all manufacturers utilized the software buttons of the Nexus. Having said that, I'll take the S4 button placement over the One. Overall, I prefer the look of the One but the S4 is a close enough second to not make a difference for ME.
FEATURES
I will not regurgitate the plethora of features from both devices as it has been discussed ad nauseam. Personally, I prefer having the options available than not. In my opinion, they are not gimmicks. They're options that you don't have to use if you choose not to. Whether the S4's features are as functional as some would like is another discussion. They can be used in some capacity for a particular situation. I give the edge to the S4 for this reason alone. Specifically, here is what I missed: Blocking mode- can you find an alternative in the play store, yes. But it is nice knowing it is built into the software. S Beam- many of my family members own S3's or Notes and it is nice being able to share music when the situation arises. The gallery of the S4 is more appealing and familiarity makes it easier to use for ME.
CAMERA
Hmm... I am not technical enough to articulate the specifics of imagery. As an average camera operator, I didn't see enough of a difference in the pictures or videos that would have tilted my decision to one phone or the other. I do enjoy the available of options for the camera on the S4. I have already dabbled with the dual camera function and it is great. My daughter gets tickled recording and watching herself already.
USER INTERACTION
This was big for me. I use my device about 50/50 for business and personal and I utilize the Google ecosystem. Pardon the hodge podge of thoughts as I speak on this topic. I enjoy the using both skins. I found the One to be a little more mature or adult as opposed to the S4. I dislike the colorful icons of the S4 (I am aware of the different launchers as well- just speaking of stock as I have Nova).
Lock Screen- Definitely the One. I used the productivity lock screen and really enjoyed how the incoming calls, messages and calendar entries are done.
Messaging- The One. I don't necessarily care for bubbles in messages. The straight forward approach of the One was perfect. I specifically like the black background with blue lettering.
Dialer- Push. Prefer the Sense version but it wouldn't tilt my decision.
Browser- Push. I use Chrome 90% of the time and didn't see a difference in speed or rendering
SCREEN
This is purely subjective. It really depends on what the end user enjoys. I don't think the majority of buyers will see the more accurate color of the One. I worked at Best Buy many, many years ago (for that lovely discount) in the TV area. The average buyer cared only for the pop of color than accuracy. No matter how much you educate or inform, they're viewing the screen and they want to be happy with what they have. I don't want this to be a discussion on PPI and what technical experts say. When I look at the screens of both, the text clarity is superb. I don't see a difference. Also, the AMOLED display is not as saturated as previous iterations. Looking at videos and pictures was equally impressive. This made it a push for me because I could live with both. The single item of difference in the screens is the overall brightness of the One over the S4. Images look painted on both screens.
MISC
Removable vs. Non Removable battery and storage is subjective as well. There is no right or wrong answer. I prefer the insurance of the removable battery. For me, it is much easier to swap a battery and go than carry a portable charging device.
In conclusion, you really can't go wrong with these devices. I hope everyone goes out and uses each phone to make a choice instead of listening to the One or S4 partisan arguments. Buy what fits you and be happy. The S4 is like those comfortable jeans you enjoy wearing. Although there are options just as good, it fits perfect when you put them on. What I've learned is if HTC softens the corners of the One, changes the button placement and provides a removable battery, I may just own one for longer than a week.