To me, angsty books are books that wallow in their depressingness. While in depressing books, the depressingness comes out of the story and events--you can wallow or not, as you will, but the depressingness remains.

I actually find angst more frustrating, because it feels more gratuitous. But depressing is more likely to give me that, "Gee, guess I'll just go jump off a bridge now" feeling when I'm through.

But that feeling can often be balanced by just how well the author manages to handle letting hope through at the end, and whether that hope is honest, and whether the reader believes in it.