Note that both like to eat RAM like no tomorrow. I haven't found a decent one that doesn't like 256MB+ after an hour's browsing.
I like how easy it is to navigate with the keyboard in elinks (though the default setup is awful, IIRC). I've set up opera to have many of the same bindings, but navigation in particular just doesn't work as well. Partly that's because there's no grid, but I think it's also just not as well designed.
I also like how elinks knows what the 'page down' function means. It either scrolls a page down (if I'm not at/below the bottom) or it doesn't (if I am). All other browsers in my experience think the bottom of the page is more important than my knowing where to start reading from.
A plus for opera is that I've actually worked out how to script it.
It uses the WebKit (Safari) engine, so it is great at rendering.
Its preferences are very smart...one of my favorites is "block images matching known ad sizes". Preferences can be saved per-site, nice for cookie management. OmniWeb also lets you create a list of regexes for things to always load and things to never load, e.g. files from known ad servers.
It has some unique features too. For example, you can "yank" any text field from a web page into its own window, at which point you can make it as big as you want. Also, its tabs show miniature web pages.
The "downside" (if you can call it that) is that the browser isn't free. But it is cheap at $15, and for something I use 100 times a day I figure I can afford it.
But I am thinking about switching from second version of Firefox to the third for dev tasks. I just did not test FireBug there and have no idea about its reliability on that version.
And for sure, I will switch one of my virtual OSes from IE7 to IE8 after its next beta because it's IE7/IE8 rendering modes support will make possible to test webapps for both versions.
Still has some problems with focus, but otherwise, really really great, and they seem to have fixed the TextArea bugs.
All of the operas after version 5 have gotten worse as well.
IE7 and IE8b are really bad--almost suprisingly bad.
+1 for Lynx (aka "other"), which hasn't gotten worse over the years, at least.
Safari for selective personal transactions (plugins, etc enabled).
Firefox for all work related stuff: Trac, RT, etc.
Camino for playing games and reading xkcd.
(I'd just vote but I can't.)