Unfunnybusiness is for anything that's not funny, or not generally lightweight in character. It's not really a rant community, and, AFAIK, PyrateJenni created it to keep the ugly sexism/racism stuff off of the wank communities. She sometimes seems to use it as her own personal soapbox, and, actually, I think a lot of other people do as well. It does not have to be fandom-related.

Fandom_lounge is a general fandom interest community, which was summed up once as "the fun linky community."

The various communities are not actually mutually exclusive. Almost everything exists as a way to "not see X on fandom_wank." (Though random_lounge exists as a way to "not see X on fandom_lounge." Oh, right, and deathwatch, which I created mostly as a joke. Oops.)

If the obscenity trials are specifically fandom-related (e.g., manga guy), it's technically not off-topic on fandom_lounge. If it's particularly depressing, skip fandom_lounge for unfunnybusiness. If it's not specifically fandom-related, you're definitely better off with random_lounge or unfunnybusiness.