I owned both devices and I wound up going the GS4. If it was only about software, I would have gone with the One. I think HTC did a better job with Sense than Samsung did with touchwiz. However, hardware for me was the deciding factor. Given that the GS4 and One are essentially the same size, the GS4 packs a much bigger screen. Yeah, I know, 4.7 to 5 doesnt sound like much, but in reality, its much bigger. I also like the weight of the GS4. Everyone complains about plastic, but I put a case on my phone, so I could really care a less. I like it light to start out with so it doesnt get too heavy when I add my case. Finally, I hated the button layout of the One. The power button placement and feel was horrific. I went through quite a bit to find a power button that I actually could feel when I pressed and I would up giving up. I also much prefer the physical home button for waking up the device. Add in the bigger battery and notification light that I can see from more than one angle and the GS4 fit my needs better.
The end.