All the early reviews of the Xperia z1 is that it trounces the S$; no surprise really as me Xperia Z is on a par (and better in many ways) than the S4...
Example:
Xperia Z1 v S4
As an Nexus user, I’d go with the Honami Xperia Z1. It’s got a really great shooter, and Sony’s camera software is great. The Snapdragon 800 is a beast, and the expandable storage is helpful if you like storing files locally. I would have liked more RAM involved, but 2GB is plenty.
I also find the Sony display better in general, but the Super AMOLED is never a bad choice. The removable battery on the Galaxy S4 comes in handy when you least expect to run out of juice, too. There’s nothing more frustrating than actually needing your device while out and about, only to find that red bar at the bottom of the battery indicator.
However, if we’re talking real-world scenarios, a truly water resistant device may be more handy than a swappable battery. Not having to shield the device from the real world may be really handy.
The turning point for me is TouchWiz, which I’m just not a fan of. I find it bulky, confusing at the wrong times, and more than a little ugly. Sony’s interface is clean, simple, and gets me where I need to be.
Xperia Z1 vs. Galaxy S4: comparison (video)