A lot of people seem to think of Opera Mini on the iPhone as a replacement for Safari on that platform, but there's also a different way of looking at it:
You don't actually have to replace the native browser to use Opera Mini, so instead of seeing this as a competition between browsers, you can see it as using the right tool for the job. Sometimes you use the the native browser, and sometimes you use Opera Mini.
Opera Mini lets you surf faster on slower connections, and cheaper when roaming or in other situations where you pay for your mobile data traffic. Opera Mini lets you get quickly to the content you need, whereas the native browser can be used for high-end Web applications.
Again: Opera Mini doesn't necessarily replace native browsers. It can also complement them.