Ironically I hadn't even realized that r/drama existed until at some point I noticed it being mentioned in r/subredditdrama threads. I'm not sure what the history between those 2 subs is (r/subredditdrama has 270K subscribers vs. r/drama's 32K). But r/drama seems to involve a lot more shitposting and personal-scale conflicts, e.g. a Prius driver having a history of anal-retentive commentary. Whereas r/subredditdrama is for when an entire forum goes apeshit. Or at least several impassioned commenters.
I think the difference in quality is actually more of a testament to how the mods run the community, even though both r/drama and r/subredditdrama have large overlap. But the latter seems to have instituted a culture of determined understatement, so threads have titles like "A visitor to /r/JapanTravel is adrift after he discovers that Japanese girls don't care about him". Whereas r/drama's current top post points to a Twitter account and has the title, "Orange ameriburger goes full retard...again"