So much better than the first, it's hard to believe it's the same game series!
BoF II, however, improves in just about every aspect where it's predecessor failed. The characters are more than one dimensional heroes, the story is much more involving and unique (still not groundbreaking, but much better than the first game), and the translation, while still not top-notch, isn't "A winner is you!"-esque.
Now, to the games merits: The shaman system, which allowed you to combine the powers of a few shamans with each of your characters to enhance their abilities (and occasionally transform them into kick-ass superman versions of their former selves) was great. It added another dimension to gameplay that I haven't really seen in a game since this one. As for the improved character development, I think the main example would have to be Nina. Every BoF game has a Nina, a winged girl (generally a princess, though not always), but in each game she plays a slightly different role than before. In the first BoF, she was the resident healer, and her character was a by-the-numbers princess who seemed very stale. In BoF II, however, her character becomes more of a tragic princess, someone cast out from their land because of a bad omen (jet-black wings), and who spends a good deal of the game trying to prove to her family that she's not going to bring destruction to their kingdom. Much better, isn't it?
BoF II does have some flaws, however...it's translation is still not great, the "build your own town" system wasn't very effective or user friendly (you couldn't evict people? Wtf was up with that?), and some parts of the story did seem to drag, mainly in the form of quests that take hours to complete (such as the huge quest that ends with you getting Spar, perhaps the least useful character in the game).
Overall, however, BoF II is an extremely good RPG, and while not on the same level as FF III/VI or Chrono Trigger, is still a game I recommend to anyone who enjoys a good SNES RPG.