Update: Just got Galaxy S4, it's laggier than iPhone 4s!
I decided not to go back to ios and give Android another chance. I returned my S4 and got an HTC One Unlocked.
I have been using One for two days and lag is noticeably less(when it lags, that is.)
The battery is not as good as it was on S4.
LCD size gets smaller because of black menu bar, most apps use.
I love how it feels in the hand! I will definitely be getting the Nexus version of One, once it's available in my country.