Do you think that Angelus really hated Buffy and that he really wanted to destroy her? Or maybe it was just a way to hide his feelings for her? Maybe he loved her and wanted to be with her, but knowing that she loves Angel and that she has to destroy him to save the world, he din't bother with it so he continued playing the "I hate all of you and I'm going to destroy the world" roll?
Angelus hates everyone. Buffy was his one of his obsessions, a human cleanser he needed to destroy at the time. He said it himself, she made Angel feel human, he couldn't let that transgression pass. Therefore he tried to punish her. It was derived from who he was as a monster.
I think the second time would have gone differently, had SHE been in ATS for those few episodes - more ass kicking of course but I doubt he'd go so far as to try and destroy the world. Just *her*. ;)!
He'd probably go so far as to turn her if he could, purely because owning something that protected the world for so long, I feel would really appeal to him.
Well...Angelus is known to be a 'player' in the emotional side of the victim and in his mind he could have done that because he thinks that he should do that... because it's his mark...or maybe a part of him loved her and I think no matter what he would do his love for her only kept growing and growing and I'm pretty sure he knew that, I mean he's always so observant that I think there was a point that he actually knew. So he wants to put an end to it...by sending the world to hell.
That's exactly how I see Angel and Spike relationship. Maybe it's a bit unconventional, but I really took it from the canon!
Updated version of the previously posted vid with some fixes (aspect ratio mostly).