B: The Beginning is a strange combination of two completely different type of stories, alternating the elements of a relatively down to earth thriller with the kind of battle scenes one would expect to see in a fantasy fighting anime (Albeit darker than stuff like Naruto or Dragon Ball Z) often giving me the impression that I was watching two completely different series merged together.
I guess that dissonance might be the cause of why this series didn't get the recognition it would have received under other kind of circumstances, since "B: The Beginning" has plenty of great elements: The animation and the designs are very good, it has an excellent atmosphere, the music is nice, and the characters are likeable and interesting.
The only weak point is the connection of the seemingly unrelated stories of Keith and Koku, which sadly isn't strong enough as it could have been, And honestly, even when the figth scenes involving Koku were quite well animated and fun to watch, I honestly would have preferred if this series focused only on Keith and the mystery plot.
if that was the case, I'm sure this show could have been a big success among the anime fandom, in a similar way to "Death Note".