Anthem? No. By the time it actually releases it could be a rhythm game about making the prettiest garden in Friendship City. Don't put your eggs in that basket, especially with EA behind it.
Nothing, not even Bungie, has [i]killed[/i] Destiny 2. Until they shut down the servers and turn off the lights, Destiny is a going and successful concern.
As far as Anthem, god knows, people love predicting "RIP Destiny when $NEW_GAME comes out!"