It could also be the way that Angel and Spike look at being turned evil.
In the episode in which the rogue slayer cuts of Spike's hands, Spike is shaken because he feels like even though he wasn't the one who killed her family, there were a lot of grieving young girls out there whom he had hurt in that way. He sympathized with the rogue slayer and felt sorry for her because now she would have to carry that same burden. Angel seemed appalled. He excused the slayer's killings because she was, in his words, "an innocent victim." Spike answered quietly, "so were we, once." I paraphrased, so my quotes may be a little off, but I think you get the idea.
Spike carries a lot of guilt for his actions. He sees being turned evil as a tragedy. Even though he was turned evil by being vamped, he sees himself as being no different from an ensouled human who is turned evil by circumstance. The soul may be easier for Spike to bear because he retained enough of his humanity that he never really felt all that far distant from it. William carried into vampire life his capacity for love, his taste for poetry, and his need to feel accepted. Even though he changed his name to Spike (a name that came from his response to criticism of his poetry), he was still that sensitive William fellow. In many ways, "Spike" was how he covered for that. Similarly, when Spike was souled, he was still Spike. That being the case, I think Spike thinks of his past as that of an evil person.
Angel also carries a lot of guilt for his actions. He sees being turned evil as an abomination. Because he was turned evil by being vamped, he sees himself as somehow being worse than or more evil than an ensouled human who is turned evil by circumstance. The soul may be harder for Angel to bear because he didn't retain enough of his humanity to ever feel close to it again. He always made huge distinctions between Liam and Angelus and between Angelus and Angel. To him, they were like three different people. It's like an unholy trinity. They're three in one. Angelus is the distilled essence of everything that is evil. Angel is the distilled essence of everything that is good. Liam was everything that was human. I think Angel thinks of his past as Angelus as being that of the embodiment of pure evil.
So, basically... what DoI said, but more long-winded-like.