With each new iPhone, it seems like apps can't open any faster, scrolling can't be any smoother and animations can't be any more fluid. Then the next iPhone launches.
The iPhone 5's software performance is better than its predecessors in nearly every conceivable way. Apple doubled the RAM to 1GB and added the new A6 chipset, with phenomenal results. This is the fastest smartphone on the market when performing common functions.
Apps open instantly. Music and video streams start immediately as long as there's a decent data connection, and there's no discernible lag when jumping from one app to another.
The iPhone 5 also gets a big speed boost thanks to LTE. I am now able to use data on an AT&T(T) iPhone in the middle of the day in midtown Manhattan, a feat that was next to impossible on AT&T's HSPA network.
The phone's battery life stronger as well. My handset is connected to Wi-Fi for most of the day at my office or at home, but with the iPhone 4S I found that I needed to charge my phone roughly every 24 hours. As I write this, it's been about 24 hours since I last charged my iPhone 5, and the battery currently reads 31%. That's a huge improvement.