I have BPD and I'm very, very different from many women who also claim to be BPD. I honestly do not get this stereotype that BPD women are abusive, raging maniacs - yeah, I feel things very, very intensely and my perspective is flawed, but with this I care about people extremely deeply and never want to hurt them. I could never abuse the people I love...what I'm more likely to do is disappear completely from their lives because I believe they're better off without me. I hate this aspect of myself. I trip over myself trying to be a "yes" person, doing favours for people, etc, because I so desperately want to be liked and was terrified of being left by the people I care about again. I'm terrified of being judged so I keep myself confined in many ways because I feel like if someone says one more thing I will implode. Apparently, this isn't the healthiest way to do thing so I finally got DBT and things are getting better slllooowwwlly.
I contrast my experience (and the experiences of a few other friends who are also diagnosed BPD) with some girls I've known who have claimed to be BPD, but have had behaviours I'd be more quick to label as histronic or anti-social (In addition to having a mental illness I'm also in school for mental health counselling). One was a compulsive liar, tried to trick her boyfriend into getting her pregnant, stole from me and my friends, hit one of my friends in the face, etc. Another pulled out a handgun at a party and started showing it off....
And that's where we get labeled as psychos. If someone is actually diagnosed ASPD, they're not likely to even believe it. They think they're misunderstood, they have something else. It's impossible for them to accept their own sociopathy so they cling to something else. But they can never truly get better unless they accept it.
One of the hallmarks of ASPD is criminal behaviour. Not to say people with BPD don't commit crimes, I'm positive we probably commit more than the "healthy" populace, but nearly all ASPD sufferers exhibit criminal behaviour, hence the name. They don't think through how their actions might have long consequences for many people, they are only thinking of themselves, and their needs/wants in moment. Somewhere along the line they've been so damaged that they have retreated completely inside themselves to become a one-person universe. As lonely as I feel with my disorder and its own stigma, I'm sure ASPD must be a million times lonelier.
TL;DR: I think the main, most factor here is that true ASPD sufferers tend to be a path of destruction towards others, whereas BPD sufferers tend to be actively destroying only themselves.