Display & Speaker Quality
In the last two months, I've been juggling the Nexus 4, Note II, Xperia Z and now the Galaxy S4. The Galaxy S4's screen is by far the best, for real-world, casual use. I don't sit on my phone all day, but when I use it, I like to enjoy it (as I'm sure everyone does). The Galaxy S4 screen is a joy to look at, with awesome viewing angles and beautiful color.
Out in the direct sunlight it's not so great, which is something I'm looking forward seeing improvements on in the coming years. We need these premium smartphones to have great display output in broad daylight, too.
Moving onto the speaker quality, I found it great. Again, I used it in real-world environments, such as when I'm sitting in a cabin in the country and need some music. I can crank it up to 75% or so and it's loud enough to listen to.
Sure, it's not the best of quality (what smartphone loudspeaker is?) but it's good enough. I used it when I was at a friend's place just hanging around having a few drinks, whipped out my Galaxy S4 and played some tunes. It was fine - it filled the room well enough for us to all hear it.