Web developer here. I use all 5 browsers. It's part of my job so I like to think I have a pretty objective viewpoint on this.
My 2013 browser ranking from lowest to highest:
5. Safari.
Nothing much has changed with Safari this year and for that reason it's falling behind in the competition. Remains meh as always. I still absolutely hate the fact that the new tab button is so hard to find compared to the other browsers. I know Apple likes to be different but you shouldn't be trying this with standard expected UI tropes. Also it still has problems with CSS that IE10 doesn't. An unfortunate drop in the rankings this year for Apple.
4. Internet Explorer.
For the first time ever, IE isn't at the bottom now that IE10 is making some marginal effort to render CSS3 properly without fault which and it actually does it pretty well. This is quite unlike IE9-7 which couldn't render CSS for shit and made life for all web developers a living hell. Still can't comment on it's speed and usability which seems to be as mediocre as always
But from a developer perspective I am appreciating it more. I like how it can preview how the older browsers fuck shit up and that's great for debugging and it forces itself on top of older version of IE so nobody gets to use IE6. New improvements in the UI of IE10 makes it easier for me to walk through clients when they call me for tech support whenever IE fails to display shit properly. Just today, one of my clients called, complaining that their website wasn't displaying in IE and it took me only 1 minute to show her where to turn off Compatibility View this time. Well done Microsoft.
3. Opera. Much improved over the last year but still not enough to make me actually use it. I want to love Opera. I really do. You know, in a root-for-the-underdog kind of way. It still has some good innovations and good UI. It even has Chromes dev tools! It's like the little browser that could. But sadly its continued lack of love, support (and prevalence of bugs) sets it back
2. Google Chrome
Formerly at the top, but unfortunately pushed down this year after recent updates made Chrome surprisingly WORSE at handling CSS3 than internet explorer!
Seriously, Chrome gave me a headache with absolutely positioned div elements and backface-visibility settings. (Since Safari runs on the same engine as Chrome, these problems affect Safari too. That's why Safari is so low) Meanwhile IE didn't have a problem at all. Absolutely fucking disgusting for Google.
But Chrome still remains a strong contender and one of my most used browsers for it's speed, stability and excellent, excellent dev environment
1. Mozilla Firefox
Firefox managed to bump out Chrome simply by not giving me any bullshit. It's now officially the browser that does not fuck up and lets me do my job. Despite being perfectly good with CSS3, it still has software glitches here and there which I noticed but hey at least it doesn't let Google, Microsoft and Apple invade my privacy
I don't need to elaborate on the rest. You guys know what makes this browser great
Congratulations Mozilla. You recieve BSOD's award for best browser of 2013.