Tiger barbs will nip the trailing fins on your angelfish. I've seen a lot of people do that.
Angels are no slouches, especially wild ones, and will be very aggressive amongst themselves. I got 12 wild scalare a few years back and they slowly killed each other off until I only had about 4 left. I tried large tanks, small tanks, species-only, community setups, bare-bottom, decorated... nothing kept them from hunting each other down and attacking.
Several of the local stores I've been to here keep larger angels in their cichlid communities with severums, oscars, chocolates, etc. I currently have some wild scalare in with my psittacus, notatus, Krobia, and chocolate cichlid. They're fine together.
My suggestion is to quarantine the angels for a few weeks until they're fiesty and eating well, then just try it. You may be surprised. Watch them for a bit, and if it starts to get heated, just move them again and find a more peaceful SA to keep them with.