If you have no experience with the Buffy and Angel TV shows, this will lose you completely. It also will be a bit spoiler-y. I'm not even going to try to review what I say for that aspect. So, if you haven't watched the whole series and plan to, you might want to finish that before you read this. On the other hand, if you read what I've written, you may better be able to analyze its truth as you watch.
I've been thinking and pondering and, recently, debating/discussing with my brother the core personality traits of the two main vampires in the Buffy/Angel TV shows. They stand apart in major ways from ALL of the "background" vampires. I wanted to know what was it about them as individuals that made them so different. In doing this analysis, I think I've also figured out why I like Spike better... but more on that later. I started with Spike, because he's my favorite and he's relatively easy.
But, before I explain, let me give you the rules I was trying to follow. To be a core trait, it must be something that was present in the individual before they became a vampire and remained present throughout their vampiric life (both good and evil). There were some snags along the way as I tried to fit various explanations into that rule, but I think I may have it nailed down now.
Spike is, at his core, a poet and a romantic. This is easy to see as a human. It's not too hard to see in his relationships with Dru and Buffy throughout his vampiric life. But it becomes a bit tough to explain some of his actions in that light. However, I believe I have an explanation (and I don't think it's a cop-out, though you may disagree). Because this romantic poet nature isn't ideal for survival as a vampire, Spike intentionally decided to follow a course of reckless violence. He didn't really have much of a heart for it, though he did develop a taste after it became a habit. This habit (formed over HUNDREDS of years) was hard to break, and it took the implanting of the anti-violence chip for him to leave it behind... though that still doesn't make a habit easy to break. It's quite possible that his being required to act against his core nature is an explanation for his almost suicidal pursuit of Slayers. And that same violation of his nature is why he had such a problem with his returned soul, it made him insane (though I'm sure the meddling of the First had a lot to do with it too). Sacrificing himself for his love fits perfectly with his personality, and his return in the Angel series would be frustrating as it conflicts with the poetry of his sacrifice.
Angel was much harder. To find his core you must reconcile his basically hedonistic ways as a human with his artistry as Angelus with his rat-eating Angel phase prior to Whistler's intervention with his super-hero Angel phase after teaming up with Buffy. My brother and I tried to stick various things in, but none of them fit, as they conflicted with at least one of his phases. But I think we finally found it when we ended up with selfish, immature, and prideful. As a human, these all fit... his pride being the hardest to see, but it is what kept him from trying overly hard to please his father. As Angelus they are fairly obvious... the immaturity a bit less so. Rat eating Angel we'll get back to. Super-hero Angel is all of the above, but from the point of his introduction to Buffy, she becomes a part of his self-interest, so his protection of her is essentially selfish. Rat-eating Angel is the conflicted stage for him. His pride is mangled by the return of his soul, and he doesn't manage to find a method to repair it on his own. His alliance with Buffy repairs his pride, and because of that, her presence as part of his self-interest makes sense. Early in his Angel phase (before re-becoming Angelus the first time), selfishness motivates him as he tries to ease the pain in his soul. After he realizes the impossibility of that goal, his pride takes over his motivation. Immaturity is easy to see throughout his existence, but none more so than his pouting over Spike's returned soul. The artistry of Angelus' crimes bear testament to his pride and immaturity. He plays with his victims for fun, and takes pride in his ability to play them.
I think I have covered all the bases here. If I've missed something, please let me know so I can revise my opinion or figure out how it fits.