I'm going to have to go with Cordelia Chase as the character with the most development. When were introduced to her in the pilot episode of BTVS, we have seen her act like a stuck up teen. Not a normal one. A stuck up cheerleader who didn't care about anyone and their feelings at all. She only cared about her image and popularity. By the time that season ended and season 2 was in the middle. We actually started to see Cordelia show some more personality. Started caring about things and eventually fell for Xander. That is when we we saw more change. But by the time Season 3 ended, she got really heartbroken because Xander cheated on her with his best friend Widow. We then seen a glimpse of pissed off Cordelia and a cold one too. I mean you would too if you were in the same boat as her.
By the time Angel series hits we seen Cordelia actually become one of the most important character on the show. Not a side character to the main character. But an actually equal character to the main one. She had a lot of changes and development on the show. Hell, she even started to be nice to Buffy in one of the first 10 episodes. Cordelia even helped Angel start an agency on helping people and helped him throughout the series.