Performance of course is better than S3 by a wide margin. Just see the benchmark figures to have an idea :
Quadrant 12000-13000 vs 6000+ ; AntuTu 21000-22000 vs 15000-16000. Well these are just numbers but you gotta feel the additional increase in performance only when you are using it

Battery life : I estimate it at least 50 % better as the battery size alone is about 20+ % bigger. And with its lower chip operating at 1.2 Ghz for most commonly used tasks ( eg call, SMS, tweets etc ) this will be an additional advantage. Phone still new and cannot give you exact numbers. Example just 3G/H browsing, battery drain is 15-18%/hour ( download speeds at 4000-5000 kbps Maxis) vs 25-30% on the S3. And the S4 is very , very obviously cooler in operation vs the obviously hotter S3 , another contributing factor to better battery life

Display you gotta see for yourself to be impressed - must say this is Samsung finest I have seen
Camera - it is 13 MP vs 8 MP : I'd say the improvement might be not much but the added camera features is great and these depends whether you want to use it or not only

Finally had a chance test out LTE S600 edition of S4 at Singapore + previous test out on local non LTE Exynox version.

Here my first impression of S600 LTE S4 v/s Exynox No LTE S4 v/s HTC One

• Smoothness - Exynox version is more smoother and better than S600. But both version more opening apps more worst especially the S600 edition, the lagging became obvious. Don't said factory reset solved it as I also test out 3 units HTC One today, never face lagging issue at all. Me and my friend both disappointed on S4 smooth performance. I can only said too much bloatware at S4 which slow down everything. HTC One was extremely smooth nearly every part and never slow down.
  
• Camera - S4 camera awesome, it capture really great quality and it user friendly UI is great than HTC UI. I don't like HTC one camera UI. The photo capture by HTC One also not good even view inside phone.
  
• Launcher - S4 launcher as usual awesome (don't talk on performance, I mean it functionality and friendly). I don't like HTC One new sense 5 app drawer, the big clock and weather at app drawer is redundant useless. The vertical scroll of HTC One app drawer make me feel like back to gingerbread time, vertical scroll is not practical at all.
  
• Power button - HTC One power button position is extremely fail decision, they is no way you can switch off by one hand for most user as most human is right handle.
  
• Screen - Both phone is awesome, but I more prefer S4 one, it just too nice to keep looking at it.
  
• Loud speaker - HTC One speaker is the best so far I ever heard in phone.
  
• Heat - HTC One is too heat for me, S4 really cool in this part.
  
• Status Bar - I can't accept till now, HTC still decide no toggles when pull down the status bar. This make switching on off toggles too troublesome.
  

After try out both phone, I feel lucky didn't buy HTC One, it is not my daily wish phone, too many part I dislike HTC One. S4 beside similar S III design and smoothness issue, S4 is a much better choice for daily use. HTC still lost in user friendly design.

My current phone is Xperia Z, I still find it the most balance among all. It smoothness is still good even it came with the slowest spec, at least it not slow down like S4. It user friendly not as great as S4 but still wasn't bad as HTC One.

If anyone ask me which phone to buy, I will suggest either Xperia Z or S4. Sorry I won't recommended HTC One due to it few drawback especially on user friendly. But if you ask me which phone did the most smooth UI, it gonna be HTC One.