If we're putting stories on a shit scale, then I'd consider Borderland's story a few calibers above Destiny's in terms of quality. I agree that I wasn't enthralled by much that happened, but it had a plethora of personalities you could easily name after putting down the controller. A few years after playing it I can remember Tiny Tina, Claptrap Handsome Jack, Moxie, Scooter, that Hunting guy... even if I didn't enjoy all of their personalities, there was a clear story to be had.
Destiny doesn't have much of that. I can't name a single character in its universe. The queen, her brother, the stranger, and Dinklage are the only that come to mind, and even they have personalities that are as bland as paint. Only one of them had a significant chunk of dialogue, whereas I felt as if I knew the characters of Borderlands 2 pretty well.
I also think, like you said, that not taking yourself seriously makes a bad story a lot better. The overly somber tone Destiny takes on seems like it's insisting on its own importance: when the score starts riling up in the last cutscene as if you've just concluded some sort of mighty tale, I was almost rolling my eyes. At least if something dumb happens in Borderland's Story I can shrug and think "It's not supposed to be a 100% serious and believable world." In Destiny, they're treating their own Universe like a pretty big deal.
This. I'm tired of people putting down Borderlands 2's story.
Well said.