Seen many reviews, and they all show the new Z1 Hitomi to be far more powerful than the S4, with a better screen, better camera and better HD video too.
Here's some quotes:
In short: It's an absolute monster. I fired up the Geekbench 2 benchmark test and was quickly given a score of 3,706, far outstripping the S4's 3,087. That makes the Z1 the most powerful Android device I've ever tested, giving scores rivalling some lower-end laptops
Side by side with the Galaxy S4, it doesn't have the same eye-popping colour saturation, but I actually preferred the Z1's more natural tones -- the S4 can be over the top at times. It's incredibly sharp, with even the smallest text looking crystal clear and the snow flurries and mountain ridges on were displayed with breathtaking clarity.
Similarly on the Quadrant benchmark, it achieved a whopping 17,825 -- a big step above the S4's 11,381. Needless to say, it whups the proverbial of its predecessor.
CNET UK
Not happy with the best camera phone? Wanna add a big lens? No problem:
iphone 5s
Samsung S4
HTC One
Hitomi is here, the Xperia Z1 - the best phone available (as long as you don't wanna make calls; smartphones aren't too good for making phonecalls...).