Here's a hands-on test to see how much faster the iPhone 4 is compared with its predecessor, the iPhone 3GS. Take a look at the video below, and you'll see that launching apps takes about the same on both models, only slightly faster on the iPhone 4.
Multitasking, more accurately known as fast app switching, happens at about the same speed, too. The most welcome change is the iPhone's new faster Wi-Fi, 802.11n, compared with 802.11g on the iPhone 3GS. In our case, the Wi-Fi speed difference was profound. Your mileage may vary.
(iPhone 3GS is on the left, iPhone 4 on the right)