Guys, I see your "Spike throwing himself on a cross" and raise you an "Angel sitting on top of a hill waiting for the sun to rise so he can burn to a crisp/crying." 😉
Honestly, I think we need to cut them both some slack; dealing with the reality that you've slaughtered thousands seems like quite a lot to handle. They can't all reflect on their time as monsters which such nonchalance as Anya does! Personally I'd say they bring just the right amount of drama, considering.
Funny thing is that considering all of the horrors of the world these characters live in, I give them all a pass for being dramatic at various times. Yes, even Dawn. Girl had a horrible life! That's what makes Buffy so incredible; even though she occasionally lets herself have a cathartic moment in which she embraces the horror of her experiences and lets herself get into it, she is always quick to snap right back out of it, (always within the course of an episode), and get right back down to business.