Angel and Edwards Brooding (although Angels is much Sexier)
Drusilla and Alice both shunned for visions and then turned
Oz and Jacob both become werewolves and then run away
Angel and Edward both leave because they believe it is best for their girl
The scenes when the leading men leave are quite similar in dialog

There are more but I can't think of them at the moment.

mimialliwell is right about the dialogue in the break-up scenes!
Also: Teenage girl moves to a small town with their single parent and falls in love with a vampire.
The parent is usually clueless.
Angel's relationship angst is sometimes reminiscent of Edward.
In Earshot, Buffy can read everyone's mind except Angel's.
Buffy and Bella would both die for the people around them, although in very different ways.