Oooh, fun topic! I have thought extensively on this, and come to this conclusion...
I believe Angel possesses traits of both archetypes.
What do I mean by this?
Angel is no saint. He possesses many traits of an antihero. But no one can argue that Angel has and does exhibit heroic acts. He is courageous, brave, and self-sacrificing. He fights for the good of humanity willingly, and until recently, seemed to believe in our inherent goodness. YET, morally, Angel often misses the mark on the hero scale. His decisions are often morally ambiguous (Lindsey, anyone?). Angel is also defined in part by his "tragic flaw", which is of course, the means in which heroes often "fall." Angel's failure of character, like Hamlet, is his gullibility. This flaw is how Twilight came about.
To be honest though, I think Angel's more of a Byronic hero than an anything. After all, his focal struggle is his constant fight against his alter-ego, the other part of himself which represents the evil inside him, Angelus. Angel is arrogant, introspective, moody, (later on) wearly and cynical, doubting his ability to make a difference and if his mission is pointless. Antihero defined.
The modern fictional hero - of which Angel is one - could simply refer to the main character of a work. Many have referred to, say, Holden Caulfield as a 'hero' even though few would define him as one.
I think in a lot of ways Angel is no hero. He's just simply a guy who was in the wrong place at the wrong time, so he rose to the occasion and dealt with the fantastic hand he was given. Ordinary guy who was given an extraordinary gift. But sometimes I'm astounded by the things Angel does. He is a truly terrific character, even if I hate him. Angel is interesting in part because his one self, Angel, embodies what is good and what he wants to be, and his alter-self, Angelus embodies the evil he is fighting against.
So, in conclusion, Angel is both a hero and an antihero. With maybe a dash of Byronic hero mixed in.
In a lot of ways, antiheros are more appealing, because they are not larger-than-life. They are not perfect. They are flawed - like us. They are not Gods but men. It's the heroes we can't relate too. Unless, of course, they fall, and then we can see ourselves in them perfectly.