Did you use the stock browser? If so, what did you not like about it?
I've tried them all. Well...most of them. At least 5 or 6 different browsers. I used each one for AT LEAST a month. All of them before I even touched the stock browser on the GS3. Just started testing stock overall (tested speed before, not bad). I have to say....I really like it. Easily the best stock browser I've ever used, word wrap issue aside, which does seem to work occasionally, which leads me to believe it will be fixed in an update. Here's the summary, feel free to ask questions...
If you really don't want stock, then I highly suggest Maxthon BY FAR. It is loaded with features and add ons, themes and gesture settings. It's the fastest, hands down. I have extensively tested this and somehow it always comes out on top, even with multiple browsers opened and compared at once. It can also pre-load the next page you'll click on automatically, to make it load instantly. The gestures, unless turned off, can be customized to just about everything. They can be done on the page itself too instead of opening a new window like Dolphin. Chrome has limited functionality and is only useful if you use Chrome on your desktop, it's also probably the slowest one I tried. Dolphin, which I used for about a year and a half on my X2/Bionic/Rezound, is LOADED with features...but a lot of them have to be downloaded from the market and I can almost guarantee you won't use most of them. Not because you'll forget or not need, but because a lot of them are just too....complicated. They show up on your app page, are another update that'll appear, and really they just clutter things up and aren't worth the hassle IMO, and most of the time you do forget them. I used them mostly for novelty value when I remembered and most of those features are on other browsers now BECAUSE dolphin made them. I also got tired of trying to move a page to the left/right and bringing open one of the slide out side menus. If you aren't consciously thinking about it and use regular strength, it'll happen each time. Just kind of frustrating. The stock browser one definitely requires MORE strength. Firefox was ok, but like Chrome just a little basic for me. Get's the job done, but isn't any faster than Dolphin or Skyfire or Boat. Skyfire and Boat are both good too, but didn't fit me as well. I liked them both equally, but I liked Maxthon and stock more. Opera I haven't used in awhile, but I hear it's still fast (has to be equal to Maxthon though) and has improved a lot. Though the ratings are hit and miss.
Just recently have I started using stock for the first time. Wow, I actually really like it. Lot's of features, pretty fast, and it's also the only browser that'll take advantage of stock functions, such as the pop out window. So, moral of the story, if you simply do not want to try stock, I cannot recommend Maxthon enough. If you really only want to use one of the 3 you mentioned, I suggest dolphin. A bit cluttered and takes time to organize and use, but it can have a lot of features and is decently fast.
Hope this helps at all.