I actually talked to Dave Ryan not too long ago about just this subject. Here's how it goes down (from what I can remember, anyway): The White Hearts as a whole fancy themselves a superhero organization. You know, non-profit, doing it for the greater good. On the other hand, there are the Black Diamonds. The black diamonds are more neutral than anything else, seeing as how they're a mercenary group. You know, do whatever needs to be done for the right price, be it the protection of a diplomat or the eradication of demons from a small town to anything in between. Probably the only thing that ties them together is that all their members are SOL users, but even the method by which they gather new members differs rather drastically.
The White Hearts, they recruit those who use SOL skillfully out in the open. The Black Diamonds usually pick up young orphans and train them in the ways of SOL. The offspring of black diamond members also become members.
Due to their extensive training, the average black diamond member is quite a bit stronger than the average white heart member, although the higher ranked members of the white hearts could hold their own against any black diamond. I forget which one has more members, but I think it's the black diamonds. Oh, and the black diamond society is quite a bit older than the white hearts.