The Opera Mini browser in extremely fast compared to the default browser.
The thing is, Opera Mini 4 isn't designed for touch phones and works very poorly on Android phones.
If you try Opera on another platform, ie on Nokia phones, it is very very fast.
Opera are currently working on Mini 5 (which you can download here
Opera Mini | The most popular mobile phone browser in the world) which will work with touch screens but there is no Android beta available yet. Apparently at a recent tech expo they showed off Mini 5 on Android.
You can get Opera Mini 5 to work on your Android phone but you have to install JAVE/J2ME Runner (from Market) on your phone first.
Although Opera Mini 5 the application runs slower as it's on a virtual machine of sorts (ie it takes a second for menus to pop up when you press a button), you can still see how quickly it can render website.
See here for more instructions
Haavard - Run Opera Mini 5 on your Android phone