Anything is better than the speed of my iPhone 3G! It's slow! I can't wait to get my iPhone 4. I've been jealous of my sister's 3GS since she got it because of the speed! Hahaha
os 3/iOS 4 is very responsive even with the 3G/3GS and has never been slow so I doubt you will tell any difference as its always been pretty instant for me.
It seems that it is slightly faster. Load times will surely improve and the UI will certainly feel snappier. I think the best comparison you would have is the iPad.
In my case, and I'm sure with many others, the iPhone 4 is going to seem extremely fast compared to our iOS 3.1.x 3G iPhones. ~400MHz, 128mb RAM compared to a 800MHz-1GHz, 256mb RAM with iOS4.
When I played with an iPad, then went back to my 3G, it seemed gongshow.
Q: Does it feel as snappy as the iPad?
A: Absolutely. Felt even snappier than the 3GS. Hard to say how it'll hold up under real world use, but I feel totally comfortable stating this is the fastest iPhone to date.
Remember it has 4x the resolution, so a faster chip will be required even for the same performance. Saying that, it's a smaller resolution than the iPad, so it won't struggle.