I've been using Mozilla and Firefox for years. I recently began using Opera Mobile on my Pocket PC. It is great--I like it so much, I bought a license--so I thought I'd give Opera a try on the desktop. Here's a little of what I think of Firefox 18.104.22.168 vs. Opera 9.24:
So far, Opera seems to consume fewer CPU cycles and less memory. I can't tell whether it's the core browser or the numerous Firefox plugins I use, but Opera seems to beat Firefox here. As part of my Go Google strategy, this is important--I'll be using the browser more and more for everyday tasks, including basic word processing.
The ability to control advertising is important to me. I don't want to view ads in general, and I get distracted by animated ads. Firefox lets me block images from any server, a very coarse-grained way to block ads. Opera lets me block individual URLs on rendered web pages, and then edit the list later, adding wildcards. With Firefox, it's all or nothing, and with Opera, it's a lot of work to build up the black list.
The Firefox Flashblock add-on is another great way to control ads and other Flash-based content. There are ways to block Flash content in Opera (see Ad blocking, above), but it's not as easy as using Flashblock on Firefox.
Firefox's search box is nice. It's easy to add new ones from the library, but it's not super-easy to customize (super-easy criterion: grandma could do it). It's easier to customize Opera's location box. I've already added search shortcuts for Merriam-Webster and IMDb (and restored Google on my PPC by editing search.ini).
I really like the Google Toolbar add-on. It simply doesn't exist for Opera, and the Google widget is not an acceptable substitute.
I can't edit full-day events in Opera!
Winner: Firefox, and, ultimately, Google Calendar is important enough to me that Firefox might just win overall because Google app's don't run adequately in Opera.
I customize Windows to use the Dvorak keyboard. Opera often switches back to QWERTY. How annoying!
Opera widgets are nice, and Firefox doesn't offer anything similar. I usually run Google Desktop and Google widgets, though, so I don't care so much about browser-based widgets.
Add-ons / Plugins
Firefox has an extensive collection of add-ons, contributed by anyone and everyone. Opera has a more controlled, probably higher quality, set of plugins. Firefox lets you shoot yourself in the foot but gives you as many different kinds of bullets as you want. Opera tries to protect you.
Both offer tabbed browser. Opera opens new tabs without switching to them by default. Firefox's Ctrl-Tab switches to the next tab by default, while Opera changes to the most recently viewed tab (annoying).
Toolbar bookmarks / Speed Dial
Firefox lets me drag URLs onto the toolbar for fast access. Opera lets me define nine speed dial shortcuts.
Foxmarks is a great tool for synchronizing for bookmarks between multiple computers. There's no easy, free way to do this with Opera.
Meebo is sloooow! in Opera. It Just Works in Firefox, and the Meebo plugin is handy.
In a split decision, Firefox wins. I want stuff to Just Work. Google app's don't just work in Opera, so I'll stick with Firefox.