Generally true. I wouldn't guarantee it. In the case of smaller fish, it really isn't aggression; it's predation. I suppose the specific strain would matter, a bit like bettas: Some strains have had the predatory urge bred out of them; others haven't.
But you can also mitigate the predation by choosing your fish carefully. In my experience, angels will eat neons, but not cardinals, lemons, or black neons, which are a bit too big for them. They won't eat fish of the phantom/serpae/diamond type, because they're the wrong shape. (Kind of like trying to swallow a porkchop whole)
As for shrimp, I'd say red cherries or ghost shrimp would probably be on the menu. Anything from amano shrimp size up is probably going to be OK.