I think with both Angel and Spike there are historical aspects to be brought in. I don't think that either of them would think in terms of "coolness".
Angel may have seen himself, in his human form, as a rebel, not conforming to the standards of his time. With his soul, he might see this as a way he got into trouble and attracted Darla's attention, so now fights against it, but the deep seated rebel comes out every so often.
With Spike, in his human form, he was a conformist of his time, living my strict Victorian standards, so in becoming a vampire, rebels against those standards.
So with Angel the human and demon are both rebels, but the soul is not.
With Spike, the human is conformist, but the demon is a rebel. When he gets his soul back, it might see the comformist as the reason he got into trouble, so embraces the rebel.
In summary, I do not think that either of them think in terms of 'Cool', but in modern times, with both have kept up with, know what it means. Angel tries to reject it, while Spike embraces it.
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Angel may have seen himself, in his human form, as a rebel, not conforming to the standards of his time. With his soul, he might see this as a way he got into trouble and attracted Darla's attention, so now fights against it, but the deep seated rebel comes out every so often.
With Spike, in his human form, he was a conformist of his time, living my strict Victorian standards, so in becoming a vampire, rebels against those standards.
So with Angel the human and demon are both rebels, but the soul is not.
With Spike, the human is conformist, but the demon is a rebel. When he gets his soul back, it might see the comformist as the reason he got into trouble, so embraces the rebel.
In summary, I do not think that either of them think in terms of 'Cool', but in modern times, with both have kept up with, know what it means. Angel tries to reject it, while Spike embraces it.