On one hand, she's actually not bad in melee. On the other, she suffers from dumb mechanics (like not being able to switch to melee while reloading, which WOULD HAVE BEEN REALLY NICE). She's not terrible at the role of "melee shotgun" (she's actually quite good at it), but the number of situations where you'd actually want a melee shotgun are quite limited.

She's basically AUG, but without the random fire mechanic. Which makes sense because she has an AUG. This logic doesn't work for any of the other girls, but shush.

If you'd like an evaluation of AUG to get an idea of how good Angelica is, here's AUG's article.