Well, in the book, he sees the head and finds it ironic that he dies with a smile on his face, since he smiled so much in life. I don't believe Anakin was a psychopath. You could argue that after his fall, he was a sociopath, but before that he was just a troubled young man who would do anything to save the woman he loves.
Well that was poor writing for the film. The actor's wooden acting didn't help much, either. TCW had some issues, too. Mace Windu, for one, was a complete deviation from how he was established in the films. How can someone overlook the fact that for 3 films (13 years) this man has disliked and not trusted Anakin, yet they're almost buddies in the TV series?
It makes no sense to show compassion at a time when you should be the most stern and focused, yet act like a dick during peacetime and after Anakin just rescued the Chancellor. I'm not saying he should've throttled Anakin to remind him who was in charge, but to completely omit a facet of his personality like that is just lazy on the writers' part.