HTC One's camera isn't bad at all. It was built that way for a purpose. You're doing the straight up Megapixel comparison between the phones.

http://www.anandtech.com/show/6747/htc-one-review/4

Every phone has its features. It's just at a point where a simple chart-by-chart comparison won't work for most people anymore. Practically every reviewer likes the One despite the fact that on paper it's a downgrade to the S4 in every way. Basically, it is like you said, the devil is in the details, but bigger is not necessarily better.

Personally, out of those three phones, I'd rather go with the HTC One only because I like the aluminum body chassis (along with how the screen looks) and the fact that their stock Android version is 50 dollars cheaper than Samsung's. The decently sized front speakers are also a plus. I very much dislike the look of the GS4 and TouchWiz which, in comparison with HTC's Sense, has less cooler whistles and doodads IMO. But ultimately I like stock Android the best.

The beats audio chip on the One is a con for me though (http://www.youtube.com/watch?v=Cdbn_pmxFic).

I haven't given the Xperia Z much of a chance, but aside from the fact that it looks aesthetically pleasing to me and I can use it while showering, I don't see much of an advantage. The GS4 came out with a water and dust resistant version, but it's slightly bigger and the audio jack is off so it won't fit most S4 cases. The Z's overlay is much more stock Android (GS4 version is TouchWiz only). So I'll pick it over Samsung because of that.

Basically, I really don't like TouchWiz. For the most part it just feels cluttered and half baked and a pain to use.