I used BB browser for a long time before I just recently re-discovered and switched over to Opera. I was just discussing this topic with a few other BB users the other day. My thoughts:
1. Pages do seem to load up quicker in general with Opera. In BB browser I have the progress bar that says loading, but with Opera it's just "Connecting" and then wham all of a sudden everything on the page is more or less loaded. With the BB browser, the items on the page come in much slower. And it really slows down when it says "requesting scripts." I really noticed the speed when I pressed the escape key to go back on a page. It's nearly instant on Opera. On the BB Browser, it's quick but less instant as it has to load up again. Oh and here's another thing, on Wikipedia, BB Browser loads up the entire page, but when you want to go to a different section of the entry, it has to load up that section even though the entire page has been loaded up. With Opera, when you click the section you want to go to, it's instant. No loading up.
2. As mentioned before, page formatting is a big difference. Opera seems to stretch things out so there's more scrolling to do. BB fills up the screen nicely and there's less scrolling.
3. One of my earliest gripes about Opera was having to go to a separate window to type text. But I've recently come to see the light with this feature. A lot of times when I'm composing a reply, the box I normally type in is really small. But with Opera and its opening up a whole new window, my text fills up the entire screen. That means less scrolling to see what I typed earlier.
4. I feel it boils down to speed+less pretty looking pages (Opera) versus slower+nicer looking pages (BB). Seeing how this is a mobile device and even with nicer looking pages, its no where near a normal page screen, I might be leaning towards Opera for its speed.
5. Forums: one of the forums I'm on has a WAP version of their site. Very convenient as things are formatted for mobile screens to begin with. But for other forums that aren't that sophisticated, I don't even bother trying to go on it with my BB Browser. It's slow and even the formatting comes out all funky. Not so with Opera. Pages load up in a decent amount of time, and things are actually formatted in a way where it's not a PIA to navigate around the site.
6. For the most part, Opera handles regular websites really well -- in both formatting and loading up the page. An exception was Facebook. For some reason, Opera just couldn't format the website correctly. I was a bit bummed about this, since I usually resorted to using the BB Browser for FB. But I just discovered that if i change the URL from Facebook | Welcome to Facebook
to m.facebook.com, I get the same great look on Opera as I did with the BB Browser.
7. I did a comparison test this morning where I loaded up a regular page for CNET.com. Opera did it in less than 15seconds (more like 10); whereas it took my BB Browser over 25seconds to load up the same page (I'm on wifi).