I absolutely LOVE Buffy. It's not necessarily the vampires that make it better than Twatlight, but the characters in general. There weren't really any "perfect" characters. They all had flaws that they needed to overcome and growing to do-right down to side characters, like Johnathon, Harmony, and even Joyce. There was actual conflict in the story lines, and not just with the "bad guys". Buffy, Willow, and Xander fought, disagreed with each other, and got on each others' nerves at times. They were human teenagers and acted like it. I love that.
The characters who had lived for centuries acted like they had. Angel, trying to cope with his soul even after a century of having it. He fell in love with Buffy, which was out of his control, and though the audience wanted the relationship to work out, it was written in the light of "Yea, this isn't some fairytale." It wasn't a perfect relationship, and it wasn't supposed to be seen as one. It was meant to be seen as dysfunctional and chaotic and terrifying, like most teenage relationships actually are. Buffy and Spike's relationship was even more dysfunctional, and was portrayed as such. It wasn't meant to be taken as rainbows and puppies. As you watched, you could see that Buffy was sleeping with him in order to escape the trauma she'd suffered. It got very dark and violent, and it was supposed to be seen that way.
Even as the plotlines grew admittedly convoluted and wangsty, you could still sympathize with the characters at least somewhat. You could see where the internal conflicts stemmed from. That is what made it such a great show. Each character's weaknesses were shown quite visibly and bluntly, but their desire to overcome them was equally shown. Basically, Joss could show. He didn't have to tell you how speshul everyone was because the characters were written to show their strengths AND weaknesses. THAT is why I love Buffy so much, and will periodically rewatch the series in its entirety, and not get bored with it. <3