Perfect thread to post my thoughts on both =D
I came away from a few hours at Best Buy impressed with both the One and GS4. This coming from someone with an iPhone bias! The GS4 made more of an impression on me, while parts of the One's design left me indifferent.
After handling the One first, I agree w/ most in that it is an amazing screen. It was crisp, bright, and sharp. Maybe it's because I prefer IPS, but I felt it was the best on the market. The phone was snappy and fast, possibly the fastest I've ever used. The biggest thing I never liked about HTC was Sense. It feels dated, and the One is no different. And when I first laid eyes on the One, it was a thing of beauty, but it felt odd in the hands. The front is smaller than the back, so the sides are slanted out (if that makes sense). This plus the plastic feel on the side made it a little awkward to use. Surprisingly I never noticed this detail in the shots of the One and no one's ever commented about it.
Moving on to the GS4, as soon as I picked it up I was blown away. While I feel the HTC One had the best display, the GS4 comes close: the colors are just amazing on this screen. The only knock on it would be that I had to tune it to full brightness to get the screen to look this good. On auto and a little dimmer and the screen didn't seem to compete w/ either the One or iPhone 5. And I have to agree w/ others that this phone has an amazing feel of quality. I'd say that it feels as good and better than my iPhone 5! I also enjoyed the Touchwiz interface a lot this time around. In terms of speed, the GS4 was really sluggish. While system things (settings, camera, photos) were ok, the phone had trouble especially in multitasking and web browsing. I found that with all the S features turned off it performed as expected from the fastest processor and GPU (altho it was only a couple minutes with it turned off). The S features just seem too gimmicky. Hovering in the web browser was hit or miss, and I can't find a use case for waving one's hand over the phone to control it b/c it is not very robust either. With S scroll, the Samsung rep was talking to me (about how the GS4 was the only 4.2.2 JB phone, the first 1080p screen, and the best camera) the web browser got stuck scrolling up and down. And I would have to agree w/ some of the reviews out there about the black version. The pattern is really obvious, so much that it made the black GS4 look tacky. But the white one looks super sleek.
For the GS4, these are just minor complaints that could be fixed w/ software. I came away thinking this is a great device, if not the best right now.
edit: posted in haste + editing in car = fail