He could be addressing the Joker, or Bruce, or Dick, or all three of them at the same time or at different parts of the song, depending on how you want to interpret things, or how metaphorical you'd like to get. Also, slashy overtones with your pairing of choice! (I'd go for Jay/Dick myself, although Jay/Bruce certainly happens in fic. ...Jay/Joker... ahaha, ew, but... I've seen creepier, more improbable things in fandom... that could be kind of fun actually, if written well, and twisted in just the right way....)
While we're on the subject of Jason and Placebo, "For What It's Worth" (look more like a girl, Brian, I dare you) reminds me of him a little bit, too, although less so. I think about 90% of that is just the bridge: No one cares when you're out on the street, picking up the pieces to make ends meet. No one cares when you're down in the gutter; got no friends, got no lover.
...Basically, I just really love that album. Even the bits that don't make me think of Batfamily.