[Galaxy S 4 General] BarryH_GEG:
Sigh. So much analysis. Here's my recap (YMMV).

Display

The SGS4 has an AMOLED display and the One has an LCD display. They behave differently. Peak brightness on a good LCD display is going to be better and the One has a good LCD display. The SGS4 has the best AMOLED display every produced and has closed the gap considerably. It's also got a lot of funky display automation (auto-brightness is brighter than manual, Auto Tone, and Adapt Display) to conserve battery which could affect certain things users do (EG: browsing) either for better or worse. No review of either display has been bad or faulted their performance. Like AMOLED? Pick the SGS4. Like LCD? Pick the One. Don't care? Make your choice based on other features as neither display will disappoint you.

Heat

The SGS4 runs hotter than the One but not as hot as the SGS3. Based on the charts puremind posted, the maximum difference is that the SGS4's 13% hotter than the One. If that makes a difference to you buy the One.

Battery

Battery life on both phones is better than all the phones that preceded them. Browsing which favors LCD because of web pages typically having lighter backgrounds means the One will last 18% longer than the SGS4. But the SGS4 does better at voice (+24%), video (+20%), and stand-by (+30% "endurance" rating). In mixed use scenarios the end result will be either phone will deliver above average battery life and since no two people use their devices the same way all the comments from outsiders mean squat to you individually.

Camera

The cameras are pretty simple to compare. The SGS4's 13MP camera is better in every scenario except low light. And the lower the light the better the One's camera performs. The One also has optical image stabilization which makes shots taken on the move better and has a faster shutter speed because of its larger photosites which is better for action shots. It also has a wider FOV if that matters to you. The SGS4's shots have 69% more detail (4MP vs. 13MP) which means you can crop and edit them at a level that's impossible with the One. HTC's current s/w has post-processing issues which all their previous cameras have had and create a "water color" affect which is especially noticeable when zoomed. Maybe it'll be corrected with updates, maybe it won't. If most of your pictures are social-sized than either camera does the job well. If you crop and edit a lot you’ll have to decide which is more important - detail or low light performance because you can’t have both.

To me, everything else is subjective including aluminum vs. plastic and TW vs. Sense and debating them is stupid because it's all just opinion. The SGS4's expandable storage and removable battery are pluses but if someone's satisfied with the One's battery life and 32/64GB of storage they really don't matter on an individual basis.

The one thing that rarely gets mentioned is that the SGS4 is on 4.2 and the One's on 4.1. 4.1 is a year old and all the OEMs have had plenty of time to work with it. 4.2 was a mess when it was deployed and it showed on the N4, N7, and N10. There's no question there's some challenges in the SGS4's s/w. Let's see how HTC's 4.2 update for the One fares. If it's flawless we can ding Samsung. If it's got issues then we can say some of them are most likely related to 4.2.

Are you looking to XDA to help you decide which is "perfect," the One or SGS4? Good luck. They both have s/w, h/w, and usability issues and aren't perfect (except in the blinded eyes of their respective fans). Both Samsung and HTC made choices about how their h/w and s/w perform and how particular features were implemented. Each will sell tens of millions of devices. To think that the decisions they each made will please all of the tens of millions equally is a tad nuts. They've both been out for long enough that their idiosyncrasies and faults are pretty well documented. Pick through them in their respective forums and figure out which you can live with and which you can't. Everything else including the diving in to minutiae means squat; although it is entertaining.