I use Dolphin and really like it. I like the tabs at the top, to quickly switch between sites.
I tried Boat, but I didn't like not being able to see my status bar at the top.
+1 more vote for Dolphin. I like the "slide out" bookmarks. Makes for very quick and easy access. I hated the stock browser and the stupid share button that was next to the bookmark button.
I use HD, don't know anything about mini or what the differences are.
OK, I just googled up dolphin hd vs mini. Seems mini gives you a slimmed down version that focuses on speed over add-ons and frills. HD has all the bells and whistles. I have never used any of the add-ons for anything serious. I tried them once or twice when I got the browser, then never again. Maybe I would be better off using mini....now you got me thinking....