I've used Dolphin HD for some time now, but every time I try to compare its features with Dolphin Mini I get frustrated, there is no clear documentation everywhere.
That said, Dolphin Mini is a version of the browser that is optimized for velocity and reduced resources use, so I came to the conclusion that Dolphin HD is the right path to go if you have a terminal with decent resources (700Mhz o more powerfull processor, 512Mb of RAM or More, 800x400 resolution, etc....) while the Mini version is here to that ones that do not have this kind of terminals or that prefer a more faster browser even at the cost of missing some features.
So with the two versions being free I choose Dolphin HD if the terminal is powerfull enough to allow you to maintain 3 or more tabs open an user flash.