For what it's worth this is what I posted in the Android thread after a brief hands on with the S4 earlier:
So just got back to work after popping into an EE shop at lunch, had a quick fondle of the GS4.
They actually had two units, one white and one black but the white one was smashed. It looked like they tightened the little cradle that holds the demo phones in place too tight and it completely cracked the screen. Consequence of the smaller bezels perhaps? The phone was off so I had a go on the black one.
First impressions - meh. Didn't like the textured look on the plastic, I thought it looked tacky and a little off putting. It felt similar to the S3, plastic innit.
They seem to have made the space at the bottom with the back/menu/home buttons smaller to accommodate the bigger screen and I found it a little difficult to adjust my hand to reach. I do, admittedly, have fairly small hands but I find my GNexus perfect for size.
I didn't find any of the slowdowns or hiccups that people seem to mention so that was good. can I just say I hate touchwiz so much, it seems even worse than the S3. The drop drop sounds when you touch things was also so irritating, I turned that off on the store's phone to do everyone a favour.
The screen was gorgeous, I am AMOLED hater number one but it looked lovely. Very crisp and sharp, lovely colours. I was very aware though that they were a bit too much, I only remembered about the colour settings the phone has now when I left so I didn't try them. Personally I stil prefer the IPS screen of the N4.
I didn't have time to try many of the features, just tried smart scroll. I found it worse than useless, I had to move my whole head down to get it to scroll and I felt like a buffoon in the shop doing that.
Overall: very meh. I couldn't, in good conscience, recommend this over a N4 or even, god forbid, an iPhone 5. It will sell gangbusters but Samsung need to town down touchwiz and improve their build materials.