I think they do bear responsibility, or at least a degree of it. It wasn't just a "demon occupying their body", unless you mean it in metaphorical sense. When you say "it's not the same man who did", I'd agree only if you mean it metaphorically, i.e. he is a changed man. They are the same person all along - as William/soulless Spike/souled Spike, or Liam/Angelus/Angel. But they have profoundly changed. The state of being a soulless vampire diminishes responsibility to a degree, in the sense of, say a serious mental illness or personality disorder would, not in the sense of being literally possessed by a demon and unable to make decisions and choices for oneself. They clearly are able to do that, or else Spike never would have decided to get his soul back.
To be honest, it's an issue that, regardless of the number of times I've watched
Buffy and
Angel, I still remain conflicted on, although my prior assertion didn't contain any ambiguity. On some occasions, I do believe that an ensouled vampire is not culpable for the actions its body took while sans soul. After all, we are told from the very beginning of
Buffy that a vampire is a demon inhabiting the corpse of a human (no "metaphorical sense"), that it is most certainly not the same person as the previous human life. Yet we also know that vampires maintain the memories of the previous human life, and furthermore that they maintain at least some vestiges of that human's personality. However, the vampire is definitely not the same person as the human; Liam was a bumbling buffoon, not the brilliant and sadistic monster that Angelus was, for example.
In the cases of Angel and Spike, I tend to think of each "stage" as separate beings, albeit with at least some shared personality traits: the human as the original person; the vampire as a demon influenced at least somewhat by the original human; and the ensouled vampire as a new person influenced by both the demon and the original human. The demon tends to be the predominant force in a vampire, with the human origins of its vestige personality influencing it in varying ways. In the case of Angelus, the demon seized on Liam's self-awareness that he was a fool and would never amount to anything in order to aspire to greatness through brutality. In the case of Spike, the demon seized on similar feelings, coupled with William's issues with rejection and his love for his mother. In the case of Harmony, arguably the only "weak" vampire we ever met, the vain and shallow nature of the vestige human personality was apparently not much for the demon to work with, since vampire Harmony only intermittently aspired to anything.
I can accept that Angel and Spike bore some responsibility, but ultimately I think Spike had the more healthy attitude in confronting it. The demon was the driving force, not whatever remained of the man. The only reason that Spike was even in a position to decide to seek a soul was the chip implanted in his brain by the Initiative; without a way for the demon to act on its instincts, and forced into situations where he spent extended periods of time with Buffy and the Scooby Gang, the vestige human personality influenced the demon to an extent that would not have occurred sans chip. Angel, of course, had the soul forced into Angelus, which may help to explain the vast time differences between "recovery" periods for Angel and Spike. For Spike, the demon arguably had been "beaten" for a change by the remnants of William's personality, stirred by a love for Buffy. Angel didn't have that luxury of an internal conflict; one moment, he was a soulless beast, and the next he was horrified by all the acts perpetrated by the demon in his body.
As I said before, I'm often conflicted on the issue. Perhaps another Buffyverse rewatch is in order...
I didn't have time yesterday to discuss this, but here it is now. I think that they are always the same being, but with a drastically changed personality. The "demon" is not some other being that comes and possessed the body (where would it come from, and where would it go afterwards?), it comes from the human personality itself. In Freudian terms, I'd describe the
"demon" roughly as the
id, and
"soul" as the
superego (conscience, internal morality compass). In season 7, the First Evil takes not just the appearance, but also the personality of the dead (or sorta kinda
dead) people it's impersonating. Everybody has a capacity for evil inside, and after they are sired, vampires usually develop that evil side, as they are driven by human id coupled with vampire bloodlust, while also stripped of their conscience and don't feel human empathy or need to stick to the human morality they still recognize on the rational level (why else would they be calling themselves evil or bad, as many of them do?). And they all retain at least some traces of their previous human personality, and all their memories. As Darla said, "What we once were informs all that we have become."
They all think of their human selves as something they once were, not as a separate being. See Holden, for instance. See Darla before and after being sired, or after she is brought back as human - there are profound changes, but she is clearly the same person. There is no doubt that Spike is the same being, same person before and after he gets his soul. His flashbacks also show that he was still a lot like William when he was first sired - it was only after a while that he developed the Spike persona. IMO, despite being an adult, William was psychologically at an adolescent level, and he was extremely repressed, in true Victorian middle class fashion, so even as a vampire, he needed some time before his sexuality, his violent urges, and everything that used to repressed came on full force.
Angel was the only one whose duality was played as being two different people - but even that was only in season 2, and even that very inconsistently. I'd argue that there is a lot of evidence in season 2 that Angel and Angelus are the same being - most of all, the fact that "Angelus" doesn't think of "Angel" as a different person and always talks (to Spike and Dru) about "Angel"'s experiences as his own ("She made me feel human, it's something you don't forgive"). It's mostly just Buffy who likes to believe that they are two separate beings ("Now my boyfriend is gone, and the demon wearing his face is killing my friends") - and she had obvious reasons to stick to this as a defense mechanism. The scene in "Becoming pt 2" is the only instance that really makes it seem like they are 2 beings, which muddies the waters - but everything else we see on BtS before and after, and especially on AtS, contradicts it. We see that Angel remembers everything he did as Angelus pre-curse, as well, so it wouldn't make sense if he didn't remember what he did as Angelus in S2. I suppose we could see him as split personality, based on "Becoming pt 2". But it still doesn't work, due to the fact that he has all the memories. And furthermore, there are instances where Angel acts like Angelus - for instance, in "What's My Line" when he's taunting Spike, or when he's pretending to be Angelus a bit too convincingly in "Enemies"; and Angelus seems to have some of the same traits as Angel, but in a more disturbing and evil fashion: Angel's romantic obsession with Buffy (from the moment he sees her, and before she even knows him) could be correctly described as stalking, and is mirrored in a much more threatening way when he stalks and terrorizes her family and friends after he loses his soul. Angelus' devotion to causing mental suffering to people and destroying souls, one by one, is a negative version of Angel's devotion to helping people and saving souls, one by one. But he uses the same insight and empathy (empathy, not sympathy) in both cases. Look at the horrible scene where Giles finds Jenny - it's a work of someone who can imagine how Giles would feel going up those stairs, hoping to make love with the woman of his dreams, and then having all his dreams crushed, finding her dead. Is it a coincidence that it's the work of a guy whose perfect happiness, just a little earlier, came when he was making love for the first time with the woman he was madly in love with?
As for Liam being a bumbling buffoon, I don't think he was stupid, I think he was just full of insecurities and self-loathing due to his contentious relationship with his father. Becoming a vampire, he let loose all his resentment by first killing his family, and telling his father that he has finally
made something of himself - he thought he could only be "someone" as a villain. But he wasn't always the brilliant monster we see later, I think that years of experience (and learning from Darla) made the difference. When we see Angel(us) in the 1760 flashback when Darla takes him to see the Master, he is halfway between Liam and Angelus we know: he is still very cocky, reckless and rebellious. (100 years later, he will be the cautious mature one, with Spike now one-upping him in rebellious and reckless antics, and mocking him for his cautiousness.) Also, when Angel first got re-souled, he was a complete wreck, living as useless bum for a long time, and even after he goes to LA and forms Angel Investigations, there are still some traces of Liam in Angel - he can be very goofy and can make some very bad blunders when trying to be heroic. And don't forget that Angel lost his soul in S2 for the same reason Liam lost his human life and became a vampire - giving in to his sex drive and losing his head over a beautiful small, blonde woman. There are many parallels and contrasts in his relationships with those two women, and I'd say that one of the reasons he fell in love with Buffy was that he saw her as anti-Darla. Darla was his teacher in evil, Buffy was his muse for good.
But years and years of experience and everything he's been through have made him into a very different and more mature person than Liam was. However, on some level he is still doing the same thing he always has - trying to prove himself: first he was proving that he can be someone, not a useless nobody, then that he can be a good man and a hero.