That's only after Angel was made to look like an idiot and she threatened to put them both in the hospital.I don't see that. In "Sanctuary", neither backs down, while in "Yoko Factor", they both apologize to each other, so there is no clear cut winner either time. Buffy does actually get her way in "Sanctuary", when Faith turns herself over to the police. And Angel gets to beat up his replacement on BtVS and make him look like a complete idiot when Buffy takes Angel out to the corridor.
And Spike is often a comical character on BtVS. On AtS he gets to beat up Angel, who used to humiliate him on BtVS.
Spike attacks Angel with a 2by4 and gets beaten up before he is outsmarted first by Doyle and Cordy then by Marcus. He then caps it all of by setting himself on fire. That's not competent 🤓